Nagoya Mathematical Journal Articles (Project Euclid)
http://projecteuclid.org/euclid.nmj
The latest articles from Nagoya Mathematical Journal on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTTue, 31 May 2011 10:19 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
http://projecteuclid.org/
Hilbert-Samuel polynomials for the contravariant extension functor
http://projecteuclid.org/euclid.nmj/1273496983
<strong>Andrew Crabbe</strong>, <strong>Daniel Katz</strong>, <strong>Janet Striuli</strong>, <strong>Emanoil Theodorescu</strong><p><strong>Source: </strong>Nagoya Math. J., Volume 198, 1--22.</p><p><strong>Abstract:</strong><br/>
Let $(R,\mathfrak {m})$ be a local ring, and let $M$ and $N$ be finite $R$ -modules. In this paper we give a formula for the degree of the polynomial giving the lengths of the modules $\operatorname{Ext}^{i}_{R}(M,N/\mathfrak{m}^{n}N)$ . A number of corollaries are given, and more general filtrations are also considered.
</p>projecteuclid.org/euclid.nmj/1273496983_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTDeformations of elliptic fiber bundles in positive characteristichttp://projecteuclid.org/euclid.nmj/1366999807<strong>Holger Partsch</strong><p><strong>Source: </strong>Nagoya Math. J., Volume 211, 79--108.</p><p><strong>Abstract:</strong><br/>
We study the deformation theory of elliptic fiber bundles over curves in positive characteristics. As applications, we give examples of nonliftable elliptic surfaces in characteristics 2 and 3, which answer a question of Katsura and Ueno. Also, we construct a class of elliptic fibrations, whose liftability is equivalent to a conjecture of Oort concerning the liftability of automorphisms of curves. Finally, we classify deformations of bielliptic surfaces.
</p>projecteuclid.org/euclid.nmj/1366999807_Wed, 10 Jul 2013 09:07 EDTWed, 10 Jul 2013 09:07 EDTGeneric formal fibers and analytically ramified stable ringshttp://projecteuclid.org/euclid.nmj/1367242338<strong>Bruce Olberding</strong><p><strong>Source: </strong>Nagoya Math. J., Volume 211, 109--135.</p><p><strong>Abstract:</strong><br/>
Let $A$ be a local Noetherian domain of Krull dimension $d$ . Heinzer, Rotthaus, and Sally have shown that if the generic formal fiber of $A$ has dimension $d-1$ , then $A$ is birationally dominated by a 1-dimensional analytically ramified local Noetherian ring having residue field finite over the residue field of $A$ . We explore further this correspondence between prime ideals in the generic formal fiber and 1-dimensional analytically ramified local rings. Our main focus is on the case where the analytically ramified local rings are stable, and we show that in this case the embedding dimension of the stable ring reflects the embedding dimension of a prime ideal maximal in the generic formal fiber, thus providing a measure of how far the generic formal fiber deviates from regularity. A number of characterizations of analytically ramified local stable domains are also given.
</p>projecteuclid.org/euclid.nmj/1367242338_Wed, 10 Jul 2013 09:07 EDTWed, 10 Jul 2013 09:07 EDTSally’s question and a conjecture of Shimodahttp://projecteuclid.org/euclid.nmj/1369147843<strong>Shiro Goto</strong>, <strong>Liam O’Carroll</strong>, <strong>Francesc Planas-Vilanova</strong><p><strong>Source: </strong>Nagoya Math. J., Volume 211, 137--161.</p><p><strong>Abstract:</strong><br/>
In 2007, Shimoda, in connection with a long-standing question of Sally, asked whether a Noetherian local ring, such that all its prime ideals different from the maximal ideal are complete intersections, has Krull dimension at most 2. In this paper, having reduced the conjecture to the case of dimension 3, if the ring is regular and local of dimension 3, we explicitly describe a family of prime ideals of height 2 minimally generated by three elements. Weakening the hypothesis of regularity, we find that, to achieve the same end, we need to add extra hypotheses, such as completeness, infiniteness of the residue field, and the multiplicity of the ring being at most 3. In the second part of the paper, we turn our attention to the category of standard graded algebras. A geometrical approach via a double use of a Bertini theorem, together with a result of Simis, Ulrich, and Vasconcelos, allows us to obtain a definitive answer in this setting. Finally, by adapting work of Miller on prime Bourbaki ideals in local rings, we detail some more technical results concerning the existence in standard graded algebras of homogeneous prime ideals with an (as it were) excessive number of generators.
</p>projecteuclid.org/euclid.nmj/1369147843_Wed, 10 Jul 2013 09:07 EDTWed, 10 Jul 2013 09:07 EDTSharp estimates of the potential kernel for the harmonic oscillator with applicationshttp://projecteuclid.org/euclid.nmj/1371731682<strong>Adam Nowak</strong>, <strong>Krzysztof Stempak</strong><p><strong>Source: </strong>Nagoya Math. J., Volume 212, 1--17.</p><p><strong>Abstract:</strong><br/>
We prove qualitatively sharp estimates of the potential kernel for the harmonic oscillator. These bounds are then used to show that the $L^{p}-L^{q}$ estimates of the associated potential operator obtained recently by Bongioanni and Torrea are in fact sharp.
</p>projecteuclid.org/euclid.nmj/1371731682_Thu, 14 Nov 2013 09:23 ESTThu, 14 Nov 2013 09:23 ESTGenerators for modules of vector-valued Picard modular formshttp://projecteuclid.org/euclid.nmj/1371731681<strong>Fabien Cléry</strong>, <strong>Gerard van der Geer</strong><p><strong>Source: </strong>Nagoya Math. J., Volume 212, 19--57.</p><p><strong>Abstract:</strong><br/>
We construct generators for modules of vector-valued Picard modular forms on a unitary group of type $(2,1)$ over the Eisenstein integers. We also calculate eigenvalues of Hecke operators acting on cusp forms.
</p>projecteuclid.org/euclid.nmj/1371731681_Thu, 14 Nov 2013 09:23 ESTThu, 14 Nov 2013 09:23 ESTNew estimates of Hilbert–Kunz multiplicities for local rings of fixed dimensionhttp://projecteuclid.org/euclid.nmj/1375362750<strong>Ian M. Aberbach</strong>, <strong>Florian Enescu</strong><p><strong>Source: </strong>Nagoya Math. J., Volume 212, 59--85.</p><p><strong>Abstract:</strong><br/>
We present results on the Watanabe–Yoshida conjecture for the Hilbert–Kunz multiplicity of a local ring of positive characteristic. By improving on a “volume estimate” giving a lower bound for Hilbert–Kunz multiplicity, we obtain the conjecture when the ring has either Hilbert–Samuel multiplicity less than or equal to 5 or dimension less than or equal to 6. For nonregular rings with fixed dimension, a new lower bound for the Hilbert–Kunz multiplicity is obtained.
</p>projecteuclid.org/euclid.nmj/1375362750_Thu, 14 Nov 2013 09:23 ESTThu, 14 Nov 2013 09:23 ESTA note on thick subcategories of stable derived categorieshttp://projecteuclid.org/euclid.nmj/1378213591<strong>Henning Krause</strong>, <strong>Greg Stevenson</strong><p><strong>Source: </strong>Nagoya Math. J., Volume 212, 87--96.</p><p><strong>Abstract:</strong><br/>
For an exact category having enough projective objects, we establish a bijection between thick subcategories containing the projective objects and thick subcategories of the stable derived category. Using this bijection, we classify thick subcategories of finitely generated modules over strict local complete intersections and produce generators for the category of coherent sheaves on a separated Noetherian scheme with an ample family of line bundles.
</p>projecteuclid.org/euclid.nmj/1378213591_Thu, 14 Nov 2013 09:23 ESTThu, 14 Nov 2013 09:23 ESTThe structure of Sally modules and Buchsbaumness of associated graded ringshttp://projecteuclid.org/euclid.nmj/1378213590<strong>Kazuho Ozeki</strong><p><strong>Source: </strong>Nagoya Math. J., Volume 212, 97--138.</p><p><strong>Abstract:</strong><br/>
Let $A$ be a Noetherian local ring with the maximal ideal $\mathfrak{m}$ , and let $I$ be an $\mathfrak{m}$ -primary ideal in $A$ . This paper examines the equality on Hilbert coefficients of $I$ first presented by Elias and Valla, but without assuming that $A$ is a Cohen–Macaulay local ring. That equality is related to the Buchsbaumness of the associated graded ring of $I$ .
</p>projecteuclid.org/euclid.nmj/1378213590_Thu, 14 Nov 2013 09:23 ESTThu, 14 Nov 2013 09:23 ESTDivisor class groups and graded canonical modules of multisection ringshttp://projecteuclid.org/euclid.nmj/1378386543<strong>Kazuhiko Kurano</strong><p><strong>Source: </strong>Nagoya Math. J., Volume 212, 139--157.</p><p><strong>Abstract:</strong><br/>
We describe the divisor class group and the graded canonical module of the multisection ring $T(X;D_{1},\ldots,D_{s})$ for a normal projective variety $X$ and Weil divisors $D_{1},\ldots,D_{s}$ on $X$ under a mild condition. In the proof, we use the theory of Krull domain and the equivariant twisted inverse functor.
</p>projecteuclid.org/euclid.nmj/1378386543_Thu, 14 Nov 2013 09:23 ESTThu, 14 Nov 2013 09:23 ESTTriangulation of the map of a $G$ -manifold to its orbit spacehttp://projecteuclid.org/euclid.nmj/1378386544<strong>Mitsutaka Murayama</strong>, <strong>Masahiro Shiota</strong><p><strong>Source: </strong>Nagoya Math. J., Volume 212, 159--195.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a Lie group, and let $M$ be a smooth proper $G$ -manifold. Let $M/G$ denote the orbit space, and let $\pi:M\to M/G$ be the natural map. It is known that $M/G$ is homeomorphic to a polyhedron. In the present paper we show that there exist a piecewise linear (PL) manifold $P$ , a polyhedron $L$ , and homeomorphisms $\tau:P\to M$ and $\sigma:M/G\to L$ such that $\sigma\circ\pi\circ\tau$ is PL. This is an application of the theory of subanalytic sets and subanalytic maps of Shiota. If $M$ and the $G$ -action are, moreover, subanalytic, then we can choose $\tau$ and $\sigma$ subanalytic and $P$ and $L$ unique up to PL homeomorphisms.
</p>projecteuclid.org/euclid.nmj/1378386544_Thu, 14 Nov 2013 09:23 ESTThu, 14 Nov 2013 09:23 ESTDifferential operators on quantized flag manifolds at roots of unity, IIhttp://projecteuclid.org/euclid.nmj/1389111145<strong>Toshiyuki Tanisaki</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 214, 1--52.</p><p><strong>Abstract:</strong><br/>
We formulate a Beilinson–Bernstein-type derived equivalence for a quantized enveloping algebra at a root of 1 as a conjecture. It says that there exists a derived equivalence between the category of modules over a quantized enveloping algebra at a root of 1 with fixed regular Harish-Chandra central character and the category of certain twisted $D$ -modules on the corresponding quantized flag manifold. We show that the proof is reduced to a statement about the (derived) global sections of the ring of differential operators on the quantized flag manifold. We also give a reformulation of the conjecture in terms of the (derived) induction functor.
</p>projecteuclid.org/euclid.nmj/1389111145_20140522084211Thu, 22 May 2014 08:42 EDTNormal functions and the height of Gross–Schoen cycleshttp://projecteuclid.org/euclid.nmj/1389795890<strong>Robin de Jong</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 214, 53--77.</p><p><strong>Abstract:</strong><br/>
We prove a variant of a formula due to Zhang relating the Beilinson–Bloch height of the Gross–Schoen cycle on a pointed curve with the self-intersection of its relative dualizing sheaf. In our approach, the height of the Gross–Schoen cycle occurs as the degree of a suitable Bloch line bundle. We show that the Chern form of this line bundle is nonnegative, and we calculate its class in the Picard group of the moduli space of pointed stable curves of compact type. The basic tools are normal functions and biextensions associated to the cohomology of the universal Jacobian.
</p>projecteuclid.org/euclid.nmj/1389795890_20140522084211Thu, 22 May 2014 08:42 EDTStability of tautological bundles on the Hilbert scheme of two points on a surfacehttp://projecteuclid.org/euclid.nmj/1393251537<strong>Malte Wandel</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 214, 79--94.</p><p><strong>Abstract:</strong><br/>
Let $(X,H)$ be a polarized smooth projective surface satisfying $H^{1}(X,\mathcal{O}_{X})=0$ , and let $\mathcal{F}$ be either a rank 1 torsion-free sheaf or a rank 2 $\mu_{H}$ -stable vector bundle on $X$ . Assume that $c_{1}(\mathcal{F})\neq0$ . This article shows that the rank 2—respectively, rank 4—tautological sheaf $\mathcal{F}^{[2]}$ associated with $\mathcal{F}$ on the Hilbert square $X^{[2]}$ is $\mu$ -stable with respect to a certain polarization.
</p>projecteuclid.org/euclid.nmj/1393251537_20140522084211Thu, 22 May 2014 08:42 EDTSimple normal crossing Fano varieties and log Fano manifoldshttp://projecteuclid.org/euclid.nmj/1393251538<strong>Kento Fujita</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 214, 95--123.</p><p><strong>Abstract:</strong><br/>
A projective log variety $(X,D)$ is called a log Fano manifold if $X$ is smooth and if $D$ is a reduced simple normal crossing divisor on $X$ with $-(K_{X}+D)$ ample. The $n$ -dimensional log Fano manifolds $(X,D)$ with nonzero $D$ are classified in this article when the log Fano index $r$ of $(X,D)$ satisfies either $r\geq n/2$ with $\rho(X)\geq2$ or $r\geq n-2$ . This result is a partial generalization of the classification of logarithmic Fano $3$ -folds by Maeda.
</p>projecteuclid.org/euclid.nmj/1393251538_20140522084211Thu, 22 May 2014 08:42 EDTToric degenerations of integrable systems on Grassmannians and polygon spaceshttp://projecteuclid.org/euclid.nmj/1393855952<strong>Yuichi Nohara</strong>, <strong>Kazushi Ueda</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 214, 125--168.</p><p><strong>Abstract:</strong><br/>
We introduce a completely integrable system on the Grassmannian of 2-planes in an $n$ -space associated with any triangulation of a polygon with $n$ sides, and we compute the potential function for its Lagrangian torus fiber. The moment polytopes of this system for different triangulations are related by an integral piecewise-linear transformation, and the corresponding potential functions are related by its geometric lift in the sense of Berenstein and Zelevinsky.
</p>projecteuclid.org/euclid.nmj/1393855952_20140522084211Thu, 22 May 2014 08:42 EDTPointwise multipliers for Campanato spaces on Gauss measure spaceshttp://projecteuclid.org/euclid.nmj/1395747184<strong>Liguang Liu</strong>, <strong>Dachun Yang</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 214, 169--193.</p><p><strong>Abstract:</strong><br/>
In this paper, the authors characterize pointwise multipliers for Campanato spaces on the Gauss measure space $(\mathbb{R}^{n},|\cdot|,\gamma)$ , which includes $\operatorname{BMO}(\gamma)$ as a special case. As applications, several examples of the pointwise multipliers are given. Also, the authors give an example of a nonnegative function in $\operatorname{BMO}(\gamma)$ but not in $\operatorname{BLO}(\gamma)$ .
</p>projecteuclid.org/euclid.nmj/1395747184_20140522084211Thu, 22 May 2014 08:42 EDTAlmost direct summandshttp://projecteuclid.org/euclid.nmj/1395747185<strong>Bhargav Bhatt</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 214, 195--204.</p><p><strong>Abstract:</strong><br/>
We prove new cases of the direct summand conjecture using fundamental theorems in $p$ -adic Hodge theory due to Faltings. The cases tackled include the ones when the ramification locus lies entirely in characteristic $p$ .
</p>projecteuclid.org/euclid.nmj/1395747185_20140522084211Thu, 22 May 2014 08:42 EDTModular forms of half-integral weights on $\operatorname{SL}(2,\mathbb{Z})$http://projecteuclid.org/euclid.nmj/1399554604<strong>Yifan Yang</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 215, 1--66.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove that, for an integer $r$ with $(r,6)=1$ and $0\lt r\lt 24$ and a nonnegative even integer $s$ , the set \[\{\eta(24\tau)^{r}f(24\tau):f(\tau)\inM_{s}(1)\}\] is isomorphic to \[S_{r+2s-1}^{\mathrm{new}}(6,-(\frac{8}{r}),-(\frac{12}{r}))\otimes (\frac{12}{\cdot})\] as Hecke modules under the Shimura correspondence. Here $M_{s}(1)$ denotes the space of modular forms of weight $s$ on $\Gamma_{0}(1)=\operatorname{SL}(2,\mathbb{Z})$ , $S_{2k}^{\mathrm{new}}(6,\epsilon_{2},\epsilon_{3})$ is the space of newforms of weight $2k$ on $\Gamma_{0}(6)$ that are eigenfunctions with eigenvalues $\epsilon_{2}$ and $\epsilon_{3}$ for Atkin–Lehner involutions $W_{2}$ and $W_{3}$ , respectively, and the notation $\otimes({12}/\cdot)$ means the twist by the quadratic character $({12}/\cdot)$ . There is also an analogous result for the cases $(r,6)=3$ .
</p>projecteuclid.org/euclid.nmj/1399554604_20140821090913Thu, 21 Aug 2014 09:09 EDTGlobal well-posedness for a system of KdV-type equations with coupled quadratic nonlinearitieshttp://projecteuclid.org/euclid.nmj/1402319947<strong>Jerry L. Bona</strong>, <strong>Jonathan Cohen</strong>, <strong>Gang Wang</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 215, 67--149.</p><p><strong>Abstract:</strong><br/>
In this paper, coupled systems \[u_{t}+u_{xxx}+P(u,v)_{x}=0,\] \[v_{t}+v_{xxx}+Q(u,v)_{x}=0\] of Korteweg–de Vries type are considered, where $u=u(x,t)$ , $v=v(x,t)$ are real-valued functions and where $x,t\in\mathbb{R}$ . Here, subscripts connote partial differentiation and \[P(u,v)=Au^{2}+Buv+Cv^{2}\quad\mbox{and}\quad Q(u,v)=Du^{2}+Euv+Fv^{2}\] are quadratic polynomials in the variables $u$ and $v$ . Attention is given to the pure initial-value problem in which $u(x,t)$ and $v(x,t)$ are both specified at $t=0$ , namely, \[u(x,0)=u_{0}(x)\quad\text{and}\quad v(x,0)=v_{0}(x),\] for $x\in\mathbb{R}$ . Under suitable conditions on $P$ and $Q$ , global well-posedness of this problem is established for initial data in the $L^{2}$ -based Sobolev spaces $H^{s}(\mathbb{R})\times H^{s}(\mathbb{R})$ for any $s\gt -{3}/{4}$ .
</p>projecteuclid.org/euclid.nmj/1402319947_20140821090913Thu, 21 Aug 2014 09:09 EDTOn operator-valued monotone independencehttp://projecteuclid.org/euclid.nmj/1406039894<strong>Takahiro Hasebe</strong>, <strong>Hayato Saigo</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 215, 151--167.</p><p><strong>Abstract:</strong><br/>
We investigate operator-valued monotone independence, a noncommutative version of independence for conditional expectation. First we introduce operator-valued monotone cumulants to clarify the whole theory and show the moment-cumulant formula. As an application, one can obtain an easy proof of the central limit theorem for the operator-valued case. Moreover, we prove a generalization of Muraki’s formula for the sum of independent random variables and a relation between generating functions of moments and cumulants.
</p>projecteuclid.org/euclid.nmj/1406039894_20140821090913Thu, 21 Aug 2014 09:09 EDTGeneralized Lyubeznik numbershttp://projecteuclid.org/euclid.nmj/1406130497<strong>Luis Núñez-Betancourt</strong>, <strong>Emily E. Witt</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 215, 33 pages.</p><p><strong>Abstract:</strong><br/>
Given a local ring containing a field, we define and investigate a family of invariants that includes the Lyubeznik numbers but captures finer information. These generalized Lyubeznik numbers are defined in terms of $D$ -modules and are proved well defined using a generalization of the classical version of Kashiwara’s equivalence for smooth varieties; we also give a definition for finitely generated $K$ -algebras. These new invariants are indicators of $F$ -singularities in characteristic $p\gt 0$ and have close connections with characteristic cycle multiplicities in characteristic zero. We characterize the generalized Lyubeznik numbers associated to monomial ideals and compute examples of those associated to determinantal ideals.
</p>projecteuclid.org/euclid.nmj/1406130497_20140821090913Thu, 21 Aug 2014 09:09 EDTPolarized pairs, log minimal models, and Zariski decompositionshttp://projecteuclid.org/euclid.nmj/1405525767<strong>Caucher Birkar</strong>, <strong>Zhengyu Hu</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 215, 203--224.</p><p><strong>Abstract:</strong><br/>
We continue our study of the relation between log minimal models and various types of Zariski decompositions. Let $(X,B)$ be a projective log canonical pair. We will show that $(X,B)$ has a log minimal model if either $K_{X}+B$ birationally has a Nakayama–Zariski decomposition with nef positive part, or if $K_{X}+B$ is big and birationally has a Fujita–Zariski or Cutkosky–Kawamata–Moriwaki–Zariski decomposition. Along the way we introduce polarized pairs $(X,B+P)$ , where $(X,B)$ is a usual projective pair and where $P$ is nef, and we study the birational geometry of such pairs.
</p>projecteuclid.org/euclid.nmj/1405525767_20140821090913Thu, 21 Aug 2014 09:09 EDTTwo remarks on polynomially bounded reducts of the restricted analytic field with exponentiationhttp://projecteuclid.org/euclid.nmj/1405342240<strong>Serge Randriambololona</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 215, 225--237.</p><p><strong>Abstract:</strong><br/>
This article presents two constructions motivated by a conjecture of van den Dries and Miller concerning the restricted analytic field with exponentiation. The first construction provides an example of two o-minimal expansions of a real closed field that possess the same field of germs at infinity of one-variable functions and yet define different global one-variable functions. The second construction gives an example of a family of infinitely many distinct maximal polynomially bounded reducts (all this in the sense of definability) of the restricted analytic field with exponentiation.
</p>projecteuclid.org/euclid.nmj/1405342240_20140821090913Thu, 21 Aug 2014 09:09 EDTMinimal models and abundance for positive characteristic log surfaceshttp://projecteuclid.org/euclid.nmj/1410268502<strong>Hiromu Tanaka</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Advance publication, 70 pages.</p><p><strong>Abstract:</strong><br/>
We discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for $\mathbb {Q}$ -factorial surfaces and for log canonical surfaces. Moreover, in the case where the base field is the algebraic closure of a finite field, we obtain the same results under much weaker assumptions.
</p>projecteuclid.org/euclid.nmj/1410268502_20150109100341Fri, 09 Jan 2015 10:03 ESTMusielak–Orlicz Hardy spaces associated with divergence form elliptic operators without weight assumptionshttp://projecteuclid.org/euclid.nmj/1412687061<strong>Tri Dung Tran</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Advance publication, 40 pages.</p><p><strong>Abstract:</strong><br/>
Let $L$ be a divergence form elliptic operator with complex bounded measurable coefficients, let $\omega$ be a positive Musielak–Orlicz function on $(0,\infty)$ of uniformly strictly critical lower-type $p_{{\omega}}\in(0,1]$ , and let $\rho(x,t)={t^{-1}}/\omega^{-1}(x,t^{-1})$ for $x\in\mathbb{R}^{n}$ , $t\in(0,\infty)$ . In this paper, we study the Musielak–Orlicz Hardy space $H_{\omega,L}({\mathbb{R}}^{n})$ and its dual space $\mathrm{BMO}_{\rho,L^{\ast}}({\mathbb{R}}^{n})$ , where $L^{\ast}$ denotes the adjoint operator of $L$ in $L^{2}({\mathbb{R}}^{n})$ . The $\rho$ -Carleson measure characterization and the John–Nirenberg inequality for the space $\mathrm{BMO}_{\rho,L}({\mathbb{R}}^{n})$ are also established. Finally, as applications, we show that the Riesz transform $\nabla L^{-1/2}$ and the Littlewood–Paley $g$ -function $g_{L}$ map $H_{\omega,L}({\mathbb{R}}^{n})$ continuously into $L(\omega)$ .
</p>projecteuclid.org/euclid.nmj/1412687061_20150109100341Fri, 09 Jan 2015 10:03 ESTQuantum reconstruction for Fano bundles on projective spacehttp://projecteuclid.org/euclid.nmj/1415383898<strong>Andrew Strangeway</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Advance publication, 28 pages.</p><p><strong>Abstract:</strong><br/>
We present a reconstruction theorem for Fano vector bundles on projective space which recovers the small quantum cohomology for the projectivization of the bundle from a small number of low-degree Gromov–Witten invariants. We provide an extended example in which we calculate the quantum cohomology of a certain Fano 9-fold and deduce from this, using the quantum Lefschetz theorem, the quantum period sequence for a Fano 3-fold of Picard rank 2 and degree 24. This example is new, and is important for the Fanosearch program.
</p>projecteuclid.org/euclid.nmj/1415383898_20150109100341Fri, 09 Jan 2015 10:03 ESTErratum: Linear projections and successive minimahttp://projecteuclid.org/euclid.nmj/1418135930<strong>Christophe Soulé</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Advance publication, 5 pages.</p>projecteuclid.org/euclid.nmj/1418135930_20150109100341Fri, 09 Jan 2015 10:03 ESTDeformations with constant Lê numbers and multiplicity of nonisolated hypersurface singularitieshttp://projecteuclid.org/euclid.nmj/1418307267<strong>Christophe Eyral</strong>, <strong>Maria Aparecida Soares Ruas</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Advance publication, 22 pages.</p><p><strong>Abstract:</strong><br/>
We show that the possible jump of the order in an $1$ -parameter deformation family of (possibly nonisolated) hypersurface singularities, with constant Lê numbers, is controlled by the powers of the deformation parameter. In particular, this applies to families of aligned singularities with constant topological type—a class for which the Lê numbers are “almost” constant. In the special case of families with isolated singularities—a case for which the constancy of the Lê numbers is equivalent to the constancy of the Milnor number—the result was proved by Greuel, Plénat, and Trotman.
As an application, we prove equimultiplicity for new families of nonisolated hypersurface singularities with constant topological type, answering partially the Zariski multiplicity conjecture.
</p>projecteuclid.org/euclid.nmj/1418307267_20150109100341Fri, 09 Jan 2015 10:03 ESTGluing silting objectshttp://projecteuclid.org/euclid.nmj/1420815813<strong>Qunhua Liu</strong>, <strong>Jorge Vitória</strong>, <strong>Dong Yang</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Advance publication, 35 pages.</p><p><strong>Abstract:</strong><br/>
Recent results by Keller and Nicolás and by Koenig and Yang have shown bijective correspondences between suitable classes of t-structures and co-t-structures with certain objects of the derived category: silting objects. On the other hand, the techniques of gluing (co-)t-structures along a recollement play an important role in the understanding of derived module categories. Using the above correspondence with silting objects, we present explicit constructions of gluing of silting objects, and, furthermore, we answer the question of when the glued silting is tilting.
</p>projecteuclid.org/euclid.nmj/1420815813_20150109100341Fri, 09 Jan 2015 10:03 ESTCentrally symmetric configurations of integer matriceshttp://projecteuclid.org/euclid.nmj/1421763195<strong>Hidefumi Ohsugi</strong>, <strong>Takayuki Hibi</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Advance publication, 18 pages.</p><p><strong>Abstract:</strong><br/>
The concept of centrally symmetric configurations of integer matrices is introduced. We study the problem when the toric ring of a centrally symmetric configuration is normal and when it is Gorenstein. In addition, Gröbner bases of toric ideals of centrally symmetric configurations are discussed. Special attention is given to centrally symmetric configurations of unimodular matrices and to those of incidence matrices of finite graphs.
</p>projecteuclid.org/euclid.nmj/1421763195_20150120091325Tue, 20 Jan 2015 09:13 ESTde Rham cohomology of local cohomology modules: The graded casehttp://projecteuclid.org/euclid.nmj/1422282101<strong>Tony J. Puthenpurakal</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Advance publication, 21 pages.</p><p><strong>Abstract:</strong><br/>
Let $K$ be a field of characteristic zero, and let $R=K[X_{1},\ldots,X_{n}]$ . Let $A_{n}(K)=K\langle X_{1},\ldots,X_{n},\partial_{1},\ldots,\partial_{n}\rangle$ be the $n$ th Weyl algebra over $K$ . We consider the case when $R$ and $A_{n}(K)$ are graded by giving $\operatorname{deg}X_{i}=\omega_{i}$ and $\operatorname{deg}\partial_{i}=-\omega_{i}$ for $i=1,\ldots,n$ (here $\omega_{i}$ are positive integers). Set $\omega=\sum_{k=1}^{n}\omega_{k}$ . Let $I$ be a graded ideal in $R$ . By a result due to Lyubeznik the local cohomology modules $H^{i}_{I}(R)$ are holonomic $(A_{n}(K))$ -modules for each $i\geq0$ . In this article we prove that the de Rham cohomology modules $H^{*}(\partial ;H^{*}_{I}(R))$ are concentrated in degree $-\omega$ ; that is, $H^{*}(\partial ;H^{*}_{I}(R))_{j}=0$ for $j\neq-\omega$ . As an application when $A=R/(f)$ is an isolated singularity, we relate $H^{n-1}(\partial ;H^{1}_{(f)}(R))$ to $H^{n-1}(\partial(f);A)$ , the $(n-1)$ th Koszul cohomology of $A$ with respect to $\partial_{1}(f),\ldots,\partial_{n}(f)$ .
</p>projecteuclid.org/euclid.nmj/1422282101_20150126092150Mon, 26 Jan 2015 09:21 ESTNormal families of meromorphic mappings of several complex variables for moving hypersurfaces in a complex projective spacehttp://projecteuclid.org/euclid.nmj/1422366836<strong>Gerd Dethloff</strong>, <strong>Do Duc Thai</strong>, <strong>Pham Nguyen Thu Trang</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Advance publication, 37 pages.</p><p><strong>Abstract:</strong><br/>
The main aim of this article is to give sufficient conditions for a family of meromorphic mappings of a domain $D$ in ${\mathbb{C}}^{n}$ into $\mathbb{P}^{N}({\mathbb{C}})$ to be meromorphically normal if they satisfy only some very weak conditions with respect to moving hypersurfaces in $\mathbb{P}^{N}({\mathbb{C}})$ , namely, that their intersections with these moving hypersurfaces, which moreover may depend on the meromorphic maps, are in some sense uniform. Our results generalize and complete previous results in this area, especially the works of Fujimoto, Tu, Tu-Li, Mai-Thai-Trang, and the recent work of Quang-Tan.
</p>projecteuclid.org/euclid.nmj/1422366836_20150127085406Tue, 27 Jan 2015 08:54 ESTThe monodromy representation and twisted period relations for Appell’s hypergeometric function $F_{4}$http://projecteuclid.org/euclid.nmj/1430939247<strong>Yoshiaki Goto</strong>, <strong>Keiji Matsumoto</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 217, 61--94.</p><p><strong>Abstract:</strong><br/>
We consider the system $\mathcal {F}_{4}(a,b,c)$ of differential equations annihilating Appell’s hypergeometric series $F_{4}(a,b,c;x)$ . We find the integral representations for four linearly independent solutions expressed by the hypergeometric series $F_{4}$ . By using the intersection forms of twisted (co)homology groups associated with them, we provide the monodromy representation of $\mathcal {F}_{4}(a,b,c)$ and the twisted period relations for the fundamental systems of solutions of $\mathcal {F}_{4}$ .
</p>projecteuclid.org/euclid.nmj/1430939247_20150506150732Wed, 06 May 2015 15:07 EDTProjective geometry in characteristic one and the epicyclic categoryhttp://projecteuclid.org/euclid.nmj/1430939248<strong>Alain Connes</strong>, <strong>Caterina Consani</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 217, 95--132.</p><p><strong>Abstract:</strong><br/>
We show that the cyclic and epicyclic categories which play a key role in the encoding of cyclic homology and the lambda operations, are obtained from projective geometry in characteristic one over the infinite semifield of max-plus integers $\mathbb{Z}_{\max}$ . Finite-dimensional vector spaces are replaced by modules defined by restriction of scalars from the one-dimensional free module, using the Frobenius endomorphisms of $\mathbb{Z}_{\max}$ . The associated projective spaces are finite and provide a mathematically consistent interpretation of Tits’s original idea of a geometry over the absolute point. The self-duality of the cyclic category and the cyclic descent number of permutations both acquire a geometric meaning.
</p>projecteuclid.org/euclid.nmj/1430939248_20150506150732Wed, 06 May 2015 15:07 EDTThe $M$ -set of $\lambda\exp (z)/z$ has infinite areahttp://projecteuclid.org/euclid.nmj/1430939249<strong>Guoping Zhan</strong>, <strong>Liangwen Liao</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 217, 133--159.</p><p><strong>Abstract:</strong><br/>
It is known that the Fatou set of the map $\exp (z)/z$ defined on the punctured plane $\mathbb{C}^{*}$ is empty. We consider the $M$ -set of $\lambda\exp (z)/z$ consisting of all parameters $\lambda$ for which the Fatou set of $\lambda\exp (z)/z$ is empty. We prove that the $M$ -set of $\lambda\exp (z)/z$ has infinite area. In particular, the Hausdorff dimension of the $M$ -set is 2. We also discuss the area of complement of the $M$ -set.
</p>projecteuclid.org/euclid.nmj/1430939249_20150506150732Wed, 06 May 2015 15:07 EDTOn certain mean values of the double zeta-functionhttp://projecteuclid.org/euclid.nmj/1430939250<strong>Soichi Ikeda</strong>, <strong>Kaneaki Matsuoka</strong>, <strong>Yoshikazu Nagata</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 217, 161--190.</p><p><strong>Abstract:</strong><br/>
In this article we discuss three types of mean values of the Euler double zeta-function. To get the results, we introduce three approximate formulas for this function.
</p>projecteuclid.org/euclid.nmj/1430939250_20150506150732Wed, 06 May 2015 15:07 EDTRational points on linear slices of diagonal hypersurfaceshttp://projecteuclid.org/euclid.nmj/1431347888<strong>Jörg Brüdern</strong>, <strong>Olivier Robert</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 218, 51--100.</p><p><strong>Abstract:</strong><br/>
An asymptotic formula is obtained for the number of rational points of bounded height on the class of varieties described in the title line. The formula is proved via the Hardy–Littlewood method, and along the way we establish two new results on Weyl sums that are of some independent interest.
</p>projecteuclid.org/euclid.nmj/1431347888_20150511083812Mon, 11 May 2015 08:38 EDTGeneralized friezes and a modified Caldero–Chapoton map depending on a rigid objecthttp://projecteuclid.org/euclid.nmj/1431347889<strong>Thorsten Holm</strong>, <strong>Peter Jørgensen</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 218, 101--124.</p><p><strong>Abstract:</strong><br/>
The (usual) Caldero–Chapoton map is a map from the set of objects of a category to a Laurent polynomial ring over the integers. In the case of a cluster category, it maps reachable indecomposable objects to the corresponding cluster variables in a cluster algebra. This formalizes the idea that the cluster category is a categorification of the cluster algebra. The definition of the Caldero–Chapoton map requires the category to be $2$ -Calabi–Yau, and the map depends on a cluster-tilting object in the category. We study a modified version of the Caldero–Chapoton map which requires only that the category have a Serre functor and depends only on a rigid object in the category. It is well known that the usual Caldero–Chapoton map gives rise to so-called friezes , for instance, Conway–Coxeter friezes. We show that the modified Caldero–Chapoton map gives rise to what we call generalized friezes and that, for cluster categories of Dynkin type $A$ , it recovers the generalized friezes introduced by combinatorial means in recent work by the authors and Bessenrodt.
</p>projecteuclid.org/euclid.nmj/1431347889_20150511083812Mon, 11 May 2015 08:38 EDTBertini theorem for normality on local rings in mixed characteristic (applications to characteristic ideals)http://projecteuclid.org/euclid.nmj/1431347890<strong>Tadashi Ochiai</strong>, <strong>Kazuma Shimomoto</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 218, 125--173.</p><p><strong>Abstract:</strong><br/>
In this article, we prove a strong version of the local Bertini theorem for normality on local rings in mixed characteristic. The main result asserts that a generic hyperplane section of a normal, Cohen–Macaulay, and complete local domain of dimension at least 3 is normal. Applications include the study of characteristic ideals attached to torsion modules over normal domains, which is fundamental in the study of Euler system theory, Iwasawa’s main conjectures, and the deformation theory of Galois representations.
</p>projecteuclid.org/euclid.nmj/1431347890_20150511083812Mon, 11 May 2015 08:38 EDTDecay estimates for solutions of nonlocal semilinear equationshttp://projecteuclid.org/euclid.nmj/1431347891<strong>Marco Cappiello</strong>, <strong>Todor Gramchev</strong>, <strong>Luigi Rodino</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 218, 175--198.</p><p><strong>Abstract:</strong><br/>
We investigate the decay for $|x|\rightarrow\infty$ of weak Sobolev-type solutions of semilinear nonlocal equations $Pu=F(u)$ . We consider the case when $P=p(D)$ is an elliptic Fourier multiplier with polyhomogeneous symbol $p(\xi)$ , and we derive algebraic decay estimates in terms of weighted Sobolev norms. Our basic example is the celebrated Benjamin–Ono equation
\begin{equation}(0.1)\quad (|D|+c)u=u^{2},\quad c\gt 0,\end{equation} for internal solitary waves of deep stratified fluids. Their profile presents algebraic decay, in strong contrast with the exponential decay for KdV shallow water waves.
</p>projecteuclid.org/euclid.nmj/1431347891_20150511083812Mon, 11 May 2015 08:38 EDTSpherical functors on the Kummer surfacehttp://projecteuclid.org/euclid.nmj/1445345515<strong>Andreas Krug</strong>, <strong>Ciaran Meachan</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 219, 1--8.</p><p><strong>Abstract:</strong><br/>
We find two natural spherical functors associated to the Kummer surface and analyze how their induced twists fit with Bridgeland’s conjecture on the derived autoequivalence group of a complex algebraic K3 surface.
</p>projecteuclid.org/euclid.nmj/1445345515_20151020085200Tue, 20 Oct 2015 08:52 EDTLogarithmic abelian varieties, Part IV: Proper modelshttp://projecteuclid.org/euclid.nmj/1445345516<strong>Takeshi Kajiwara</strong>, <strong>Kazuya Kato</strong>, <strong>Chikara Nakayama</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 219, 9--63.</p><p><strong>Abstract:</strong><br/>
This is part IV of our series of articles on log abelian varieties. In this part, we study the algebraic theory of proper models of log abelian varieties.
</p>projecteuclid.org/euclid.nmj/1445345516_20151020085200Tue, 20 Oct 2015 08:52 EDTA McShane-type identity for closed surfaceshttp://projecteuclid.org/euclid.nmj/1445345517<strong>Yi Huang</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 219, 65--86.</p><p><strong>Abstract:</strong><br/>
We prove a McShane-type identity: a series, expressed in terms of geodesic lengths, that sums to $2\pi$ for any closed hyperbolic surface with one distinguished point. To do so, we prove a generalized Birman–Series theorem showing that the set of complete geodesics on a hyperbolic surface with large cone angles is sparse.
</p>projecteuclid.org/euclid.nmj/1445345517_20151020085200Tue, 20 Oct 2015 08:52 EDTOn modules of finite projective dimensionhttp://projecteuclid.org/euclid.nmj/1445345518<strong>S. P. Dutta</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 219, 87--111.</p><p><strong>Abstract:</strong><br/>
We address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the embeddability problem and prove important reductions and special cases of the order ideal conjecture. In particular, we derive that, in any local ring $R$ of mixed characteristic $p\gt 0$ , where $p$ is a nonzero divisor, if $I$ is an ideal of finite projective dimension over $R$ and $p\inI$ or $p$ is a nonzero divisor on $R/I$ , then every minimal generator of $I$ is a nonzero divisor. Hence, if $P$ is a prime ideal of finite projective dimension in a local ring $R$ , then every minimal generator of $P$ is a nonzero divisor in $R$ .
</p>projecteuclid.org/euclid.nmj/1445345518_20151020085200Tue, 20 Oct 2015 08:52 EDTTorsion in tensor powers of moduleshttp://projecteuclid.org/euclid.nmj/1445345519<strong>Olgur Celikbas</strong>, <strong>Srikanth B. Iyengar</strong>, <strong>Greg Piepmeyer</strong>, <strong>Roger Wiegand</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 219, 113--125.</p><p><strong>Abstract:</strong><br/>
Tensor products usually have nonzero torsion. This is a central theme of Auslander’s 1961 paper; the theme continues in the work of Huneke and Wiegand in the 1990s. The main focus in this article is on tensor powers of a finitely generated module over a local ring. Also, we study torsion-free modules $N$ with the property that $M\otimes_{R}N$ has nonzero torsion unless $M$ is very special. An important example of such a module $N$ is the Frobenius power $\mpresup{p^{e}}R$ over a complete intersection domain $R$ of characteristic $p\gt 0$ .
</p>projecteuclid.org/euclid.nmj/1445345519_20151020085200Tue, 20 Oct 2015 08:52 EDTSemiclassical orthogonal polynomial systems on nonuniform lattices, deformations of the Askey table, and analogues of isomonodromyhttp://projecteuclid.org/euclid.nmj/1445345520<strong>N. S. Witte</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 219, 127--234.</p><p><strong>Abstract:</strong><br/>
A $\mathbb{D}$ -semiclassical weight is one which satisfies a particular linear, first-order homogeneous equation in a divided-difference operator $\mathbb{D}$ . It is known that the system of polynomials, orthogonal with respect to this weight, and the associated functions satisfy a linear, first-order homogeneous matrix equation in the divided-difference operator termed the spectral equation . Attached to the spectral equation is a structure which constitutes a number of relations such as those arising from compatibility with the three-term recurrence relation. Here this structure is elucidated in the general case of quadratic lattices. The simplest examples of the $\mathbb{D}$ -semiclassical orthogonal polynomial systems are precisely those in the Askey table of hypergeometric and basic hypergeometric orthogonal polynomials. However within the $\mathbb{D}$ -semiclassical class it is entirely natural to define a generalization of the Askey table weights which involve a deformation with respect to new deformation variables. We completely construct the analogous structures arising from such deformations and their relations with the other elements of the theory. As an example we treat the first nontrivial deformation of the Askey–Wilson orthogonal polynomial system defined by the $q$ -quadratic divided-difference operator, the Askey–Wilson operator, and derive the coupled first-order divided-difference equations characterizing its evolution in the deformation variable. We show that this system is a member of a sequence of classical solutions to the $E^{(1)}_{7}$ $q$ -Painlevé system.
</p>projecteuclid.org/euclid.nmj/1445345520_20151020085200Tue, 20 Oct 2015 08:52 EDTInstability of periodic traveling waves for the symmetric regularized long wave equationhttp://projecteuclid.org/euclid.nmj/1445345521<strong>Jaime Angulo Pava</strong>, <strong>Carlos Alberto Banquet Brango</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 219, 235--268.</p><p><strong>Abstract:</strong><br/>
We prove the linear and nonlinear instability of periodic traveling wave solutions for a generalized version of the symmetric regularized long wave (SRLW) equation. Using analytic and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so the linear instability of periodic profiles is obtained. An application of this approach is made to obtain the linear/nonlinear instability of cnoidal wave solutions for the modified SRLW (mSRLW) equation. We also prove the stability of dnoidal wave solutions associated to the equation just mentioned.
</p>projecteuclid.org/euclid.nmj/1445345521_20151020085200Tue, 20 Oct 2015 08:52 EDT$p$ -adic Eisenstein–Kronecker series for CM elliptic curves and the Kronecker limit formulashttp://projecteuclid.org/euclid.nmj/1445345522<strong>Kenichi Bannai</strong>, <strong>Hidekazu Furusho</strong>, <strong>Shinichi Kobayashi</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 219, 269--302.</p><p><strong>Abstract:</strong><br/>
Consider an elliptic curve defined over an imaginary quadratic field $K$ with good reduction at the primes above $p\geq5$ and with complex multiplication by the full ring of integers $\mathcal{O}_{K}$ of $K$ . In this paper, we construct $p$ -adic analogues of the Eisenstein–Kronecker series for such an elliptic curve as Coleman functions on the elliptic curve. We then prove $p$ -adic analogues of the first and second Kronecker limit formulas by using the distribution relation of the Kronecker theta function.
</p>projecteuclid.org/euclid.nmj/1445345522_20151020085200Tue, 20 Oct 2015 08:52 EDTSome constructions of modular forms for the Weil representation of $\operatorname{SL}_{2}(\mathbb{Z})$http://projecteuclid.org/euclid.nmj/1448980485<strong>Nils R. Scheithauer</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 220, 1--43.</p><p><strong>Abstract:</strong><br/>
Modular forms for the Weil representation of $\operatorname{SL}_{2}(\mathbb{Z})$ play an important role in the theory of automorphic forms on orthogonal groups. In this paper we give some explicit constructions of these functions. As an application, we construct new examples of generalized Kac–Moody algebras whose denominator identities are holomorphic automorphic products of singular weight. They correspond naturally to the Niemeier lattices with root systems $D_{12}^{2}$ , $E_{8}^{3}$ and to the Leech lattice.
</p>projecteuclid.org/euclid.nmj/1448980485_20151201093447Tue, 01 Dec 2015 09:34 ESTRemarks on free mutual information and orbital free entropyhttp://projecteuclid.org/euclid.nmj/1448980486<strong>Masaki Izumi</strong>, <strong>Yoshimichi Ueda</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 220, 45--66.</p><p><strong>Abstract:</strong><br/>
The present notes provide a proof of $i^{*}(\mathbb{C}P+\mathbb{C}(I-P);\mathbb{C}Q+\mathbb{C}(I-Q))=-\chi_{\mathrm{orb}}(P,Q)$ for any pair of projections $P,Q$ with $\tau(P)=\tau(Q)=1/2$ . The proof includes new extra observations, such as a subordination result in terms of Loewner equations. A study of the general case is also given.
</p>projecteuclid.org/euclid.nmj/1448980486_20151201093447Tue, 01 Dec 2015 09:34 ESTA global estimate for the Diederich–Fornaess index of weakly pseudoconvex domainshttp://projecteuclid.org/euclid.nmj/1448980487<strong>Masanori Adachi</strong>, <strong>Judith Brinkschulte</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 220, 67--80.</p><p><strong>Abstract:</strong><br/>
A uniform upper bound for the Diederich–Fornaess index is given for weakly pseudoconvex domains whose Levi form of the boundary vanishes in $\ell$ -directions everywhere.
</p>projecteuclid.org/euclid.nmj/1448980487_20151201093447Tue, 01 Dec 2015 09:34 ESTApplication and simplified proof of a sharp $L^{2}$ extension theoremhttp://projecteuclid.org/euclid.nmj/1448980488<strong>Takeo Ohsawa</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 220, 81--89.</p><p><strong>Abstract:</strong><br/>
As an application of a sharp $L^{2}$ extension theorem for holomorphic functions in Guan and Zhou, a stability theorem for the boundary asymptotics of the Bergman kernel is proved. An alternate proof of the extension theorem is given, too. It is a simplified proof in the sense that it is free from ordinary differential equations.
</p>projecteuclid.org/euclid.nmj/1448980488_20151201093447Tue, 01 Dec 2015 09:34 ESTStochastic calculus over symmetric Markov processes with time reversalhttp://projecteuclid.org/euclid.nmj/1448980489<strong>K. Kuwae</strong>. <p><strong>Source: </strong>Nagoya Mathematical Journal, Volume 220, 91--148.</p><p><strong>Abstract:</strong><br/>
We develop stochastic calculus for symmetric Markov processes in terms of time reversal operators. For this, we introduce the notion of the progressively additive functional in the strong sense with time-reversible defining sets. Most additive functionals can be regarded as such functionals. We obtain a refined formula between stochastic integrals by martingale additive functionals and those by Nakao’s divergence-like continuous additive functionals of zero energy. As an application, we give a stochastic characterization of harmonic functions on a domain with respect to the infinitesimal generator of semigroup on $L^{2}$ -space obtained by lower-order perturbations.
</p>projecteuclid.org/euclid.nmj/1448980489_20151201093447Tue, 01 Dec 2015 09:34 EST