Osaka Journal of Mathematics Articles (Project Euclid)
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The latest articles from Osaka Journal of Mathematics 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, 22 Mar 2011 10:05 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Quotients of bounded homogeneous domains by cyclic groups
http://projecteuclid.org/euclid.ojm/1277298908
<strong>Christian Miebach</strong><p><strong>Source: </strong>Osaka J. Math., Volume 47, Number 2, 331--352.</p><p><strong>Abstract:</strong><br/>
Let $D$ be a bounded homogeneous domain in $\mathbb{C}^{n}$
and let $\varphi$ be an automorphism of $D$ which generates
a discrete subgroup $\Gamma$ of $\Aut_{\mathcal{O}}(D)$. It
is shown that the complex space $D/\Gamma$ is Stein.
</p>projecteuclid.org/euclid.ojm/1277298908_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTE-polynomials of $\mathrm{SL}(2, \mathbb{C})$-character varieties of complex curves of genus $3$http://projecteuclid.org/euclid.ojm/1470413983<strong>Javier Martí nez</strong>, <strong>Vicente Muñoz</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 3, 645--681.</p><p><strong>Abstract:</strong><br/>
We compute the E-polynomials of the moduli spaces of representations
of the fundamental group of a complex curve of genus $g=3$
into $\mathrm{SL}(2, \mathbb{C})$, and also of the moduli space of
twisted representations. The case of genus $g=1, 2$ has already
been done in [12]. We follow the geometric technique introduced
in [12], based on stratifying the space of representations,
and on the analysis of the behaviour of the E-polynomial under
fibrations.
</p>projecteuclid.org/euclid.ojm/1470413983_20160805121946Fri, 05 Aug 2016 12:19 EDTCompact homogeneous locally conformally Kähler manifoldshttp://projecteuclid.org/euclid.ojm/1470413984<strong>Keizo Hasegawa</strong>, <strong>Yoshinobu Kamishima</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 3, 683--703.</p><p><strong>Abstract:</strong><br/>
In this paper we show as main results two structure theorems
of a compact homogeneous locally conformally Kähler
(or shortly l.c.K.) manifold, a holomorphic structure theorem
asserting that it has a structure of holomorphic principal
fiber bundle over a flag manifold with fiber a $1$-dimensional
complex torus, and a metric structure theorem asserting that
it is necessarily of Vaisman type. We also discuss and determine
l.c.K. reductive Lie groups and compact locally homogeneous
l.c.K. manifolds of reductive Lie groups.
</p>projecteuclid.org/euclid.ojm/1470413984_20160805121946Fri, 05 Aug 2016 12:19 EDTRight-angled Artin groups and finite subgraphs of curve graphshttp://projecteuclid.org/euclid.ojm/1470413985<strong>Sang-Hyun Kim</strong>, <strong>Thomas Koberda</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 3, 705--716.</p><p><strong>Abstract:</strong><br/>
We show that for a sufficiently simple surface $S$, if a right-angled
Artin group $A(\Gamma)$ embeds into $\mathrm{Mod}(S)$ then
$\Gamma$ embeds into the curve graph $\mathcal{C}(S)$ as an
induced subgraph. When $S$ is sufficiently complicated, there
exists an embedding $A(\Gamma) \to \mathrm{Mod}(S)$ such that
$\Gamma$ is not contained in $\mathcal{C}(S)$ as an induced
subgraph.
</p>projecteuclid.org/euclid.ojm/1470413985_20160805121946Fri, 05 Aug 2016 12:19 EDTA note on the exponential decay for the nonlinear Schrödinger equationhttp://projecteuclid.org/euclid.ojm/1470413986<strong>Fábio Natali</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 3, 717--729.</p><p><strong>Abstract:</strong><br/>
We prove new results about exponential decay rates associated
with the two dimensional Schrödinger equation with critical
nonlinearity and localized damping. Our article improve incomplete
previous results established in [4].
</p>projecteuclid.org/euclid.ojm/1470413986_20160805121946Fri, 05 Aug 2016 12:19 EDTPartially ordered sets of non-trivial nilpotent $\pi$-subgroupshttp://projecteuclid.org/euclid.ojm/1470413987<strong>Nobuo Iiyori</strong>, <strong>Masato Sawabe</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 3, 731--750.</p><p><strong>Abstract:</strong><br/>
In this paper, we introduce a subposet $\mathcal{L}_{\pi}(G)$
of a poset $\mathcal{N}_{\pi}(G)$ of all non-trivial nilpotent
$\pi$-subgroups of a finite group $G$. We examine basic properties
of subgroups in $\mathcal{L}_{\pi}(G)$ which contain the notion
of both radical $p$-subgroups and centric $p$-subgroups of
$G$. It is shown that $\mathcal{L}_{\pi}(G)$ is homotopy equivalent
to $\mathcal{N}_{\pi}(G)$. As examples, we investigate in detail
the case where symmetric groups.
</p>projecteuclid.org/euclid.ojm/1470413987_20160805121946Fri, 05 Aug 2016 12:19 EDTFacets of secondary polytopes and chow stability of toric varietieshttp://projecteuclid.org/euclid.ojm/1470413988<strong>Naoto Yotsutani</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 3, 751--765.</p><p><strong>Abstract:</strong><br/>
Chow stability is one notion of Mumford's geometric invariant
theory for studying the moduli space of polarized varieties.
Kapranov, Sturmfels and Zelevinsky detected that Chow stability
of polarized toric varieties is determined by its inherent
secondary polytope , which is a polytope whose vertices
correspond to regular triangulations of the associated polytope
[7]. In this paper, we give a purely convex-geometrical proof
that the Chow form of a projective toric variety is $H$-semistable
if and only if it is $H$-polystable with respect to the standard
complex torus action $H$. This essentially means that
Chow semistability is equivalent to Chow polystability for
any (not-necessaliry-smooth) projective toric varieties.
</p>projecteuclid.org/euclid.ojm/1470413988_20160805121946Fri, 05 Aug 2016 12:19 EDTSeifert surgery on knots via Reidemeister torsion and Casson--Walker--Lescop invariant IIhttp://projecteuclid.org/euclid.ojm/1470413989<strong>Teruhisa Kadokami</strong>, <strong>Noriko Maruyama</strong>, <strong>Tsuyoshi Sakai</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 3, 767--773.</p><p><strong>Abstract:</strong><br/>
For a knot $K$ with $\Delta_{K}(t)\doteq t^{2}-3t+1$ in a
homology $3$-sphere, let $M$ be the result of $2/q$-surgery
on $K$. We show that an appropriate assumption on the Reidemeister
torsion of the universal abelian covering of $M$ implies $q=\pm
1$, if $M$ is a Seifert fibered space.
</p>projecteuclid.org/euclid.ojm/1470413989_20160805121946Fri, 05 Aug 2016 12:19 EDTA pairwise independent random sampling method in the ring of $p$-adic integershttp://projecteuclid.org/euclid.ojm/1470413990<strong>Hiroshi Kaneko</strong>, <strong>Hisaaki Matsumoto</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 3, 775--798.</p><p><strong>Abstract:</strong><br/>
For the ring of $p$-adic integers, $p$ being a fixed prime,
any sequence which plays a similar role to Weyl's irrational
rotation has not been proposed yet. We will see that a modified
$p$-adic van der Corput sequence provides us with a reasonable
counterpart of Weyl's irrational rotation in the ring. We will
present a similar random Weyl sampling on the ring to the one
proposed by Sugita and Takanobu. In the process of establishing
the counterpart, a sampling method based on a function with
naturally extended domain to the field of $p$-adic numbers
in terms of the additive characters will be mentioned.
</p>projecteuclid.org/euclid.ojm/1470413990_20160805121946Fri, 05 Aug 2016 12:19 EDTBehavior of solutions for radially symmetric solutions for Burgers equation with a boundary corresponding to the rarefaction wavehttp://projecteuclid.org/euclid.ojm/1470413991<strong>Itsuko Hashimoto</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 3, 799--811.</p><p><strong>Abstract:</strong><br/>
We investigate the large-time behavior of the radially symmetric
solution for Burgers equation on the exterior of a small ball
in multi-dimensional space, where the boundary data and the
data at the far field are prescribed. In a previous paper [1],
we showed that, for the case in which the boundary data is
equal to $0$ or negative, the asymptotic stability is the same
as that for the viscous conservation law. In the present paper,
it is proved that if the boundary data is positive, the asymptotic
state is a superposition of the stationary wave and the rarefaction
wave, which is a new wave phenomenon. The proof is given using
a standard $L^{2}$ energy method and the characteristic curve
method.
</p>projecteuclid.org/euclid.ojm/1470413991_20160805121946Fri, 05 Aug 2016 12:19 EDTOn deformations of isolated singularities of polar weighted homogeneous mixed polynomialshttp://projecteuclid.org/euclid.ojm/1470413992<strong>Kazumasa Inaba</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 3, 813--842.</p><p><strong>Abstract:</strong><br/>
In the present paper, we deform isolated singularities of
$f\bar{g}$, where $f$ and $g$ are $2$-variable weighted
homogeneous complex polynomials, and show that there exists
a deformation of $f\bar{g}$ which has only indefinite
fold singularities and mixed Morse singularities.
</p>projecteuclid.org/euclid.ojm/1470413992_20160805121946Fri, 05 Aug 2016 12:19 EDT$p$-local stable splitting of quasitoric manifoldshttp://projecteuclid.org/euclid.ojm/1470413993<strong>Sho Hasui</strong>, <strong>Daisuke Kishimoto</strong>, <strong>Takashi Sato</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 3, 843--854.</p><p><strong>Abstract:</strong><br/>
We show a homotopy decomposition of the $p$-localized suspension
$\Sigma M_{(p)}$ of a quasitoric manifold $M$ by constructing
power maps. As an application we investigate the $p$-localized
suspension of the projection $\pi$ from the moment-angle complex
onto $M$, from which we deduce its triviality for $p>\dim
M/2$. We also discuss non-triviality of $\pi_{(p)}$ and $\Sigma^{\infty}\pi$.
</p>projecteuclid.org/euclid.ojm/1470413993_20160805121946Fri, 05 Aug 2016 12:19 EDTGlobal solvability for double-diffusive convection system based on Brinkman--Forchheimer equation in general domainshttp://projecteuclid.org/euclid.ojm/1470413994<strong>Mitsuharu Ôtani</strong>, <strong>Shun Uchida</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 3, 855--872.</p><p><strong>Abstract:</strong><br/>
In this paper, we are concerned with the solvability of the
initial boundary value problem of a system which describes
double-diffusive convection phenomena in some porous medium
under general domains, especially unbounded domains. In previous
works where the boundedness of the space domain is imposed,
some global solvability results have been already derived.
However, when we consider our problem in general domains, some
compactness theorems are not available. Hence it becomes difficult
to follow the same strategies as before. Nevertheless, we can
assure the global existence of a unique solution via the contraction
method. Moreover, it is revealed that the global solvability
holds for higher space dimension and larger class of the initial
data than those assumed in previous works.
</p>projecteuclid.org/euclid.ojm/1470413994_20160805121946Fri, 05 Aug 2016 12:19 EDTMeasure-expansive homoclinic classeshttp://projecteuclid.org/euclid.ojm/1475601821<strong>Keonhee Lee</strong>, <strong>Manseob Lee</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 873--887.</p><p><strong>Abstract:</strong><br/>
Let $p$ be a hyperbolic periodic point of a diffeomorphism
$f$ on a compact $C^{\infty}$ Riemannian manifold $M$. In
this paper we introduce the notion of $C^{1}$ stably measure
expansiveness of closed $f$-invariant sets, and prove that
(i) the chain recurrent set $\mathcal{R}(f)$ of $f$ is $C^{1}$
stably measure expansive if and only if $f$ satisfies both
Axiom A and no-cycle condition, and (ii) the homoclinic class
$H_{f}(p)$ of $f$ associated to $p$ is $C^{1}$ stably measure
expansive if and only if $H_{f}(p)$ is hyperbolic.
</p>projecteuclid.org/euclid.ojm/1475601821_20161004132358Tue, 04 Oct 2016 13:23 EDTTautological sheaves: Stability, moduli spaces and restrictions to generalised Kummer varietieshttp://projecteuclid.org/euclid.ojm/1475601822<strong>Malte Wandel</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 889--910.</p><p><strong>Abstract:</strong><br/>
Results on stability of tautological sheaves on Hilbert schemes
of points are extended to higher dimensions and to the restriction
of tautological sheaves to generalised Kummer varieties. This
provides a big class of new examples of stable sheaves on
higher dimensional irreducible symplectic manifolds. Some
aspects of deformations of tautological sheaves are studied.
</p>projecteuclid.org/euclid.ojm/1475601822_20161004132358Tue, 04 Oct 2016 13:23 EDTOn Castelnuovo theory and non-existence of smooth isolated curves in quintic threefoldshttp://projecteuclid.org/euclid.ojm/1475601823<strong>Xun Yu</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 911--918.</p><p><strong>Abstract:</strong><br/>
We find some necessary conditions for a smooth irreducible
curve $C\subset \mathbb{P}^{4}$ to be isolated in a smooth
quintic threefold. As an application, we prove that Knutsen's
list of examples of smooth isolated curves in general quintic
threefolds is complete up to degree 9.
</p>projecteuclid.org/euclid.ojm/1475601823_20161004132358Tue, 04 Oct 2016 13:23 EDTIll-posedness issue for the drift diffusion system in the homogeneous Besov spaceshttp://projecteuclid.org/euclid.ojm/1475601824<strong>Tsukasa Iwabuchi</strong>, <strong>Takayoshi Ogawa</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 919--939.</p><p><strong>Abstract:</strong><br/>
We consider the ill-posedness issue for the drift-diffusion
system of bipolar type by showing that the continuous dependence
on initial data does not hold generally in the scaling invariant
Besov spaces. The scaling invariant Besov spaces are $\dot{B}_{p, \sigma}^{-2+ n/p} (\mathbb{R}^{n})$ with $1 \leq p, \sigma
\leq \infty$ and we show the optimality of the case $p = 2n$
to obtain the well-posedness and the ill-posedness for the
drift-diffusion system of bipolar type.
</p>projecteuclid.org/euclid.ojm/1475601824_20161004132358Tue, 04 Oct 2016 13:23 EDTQuasi-sure existence of Gaussian rough paths and large deviation principles for capacitieshttp://projecteuclid.org/euclid.ojm/1475601825<strong>H. Boedihardjo</strong>, <strong>X. Geng</strong>, <strong>Z. Qian</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 941--970.</p><p><strong>Abstract:</strong><br/>
We construct a quasi-sure version (in the sense of Malliavin)
of geometric rough paths associated with a Gaussian process
with long-time memory. As an application we establish a large
deviation principle (LDP) for capacities for such Gaussian
rough paths. Together with Lyons' universal limit theorem,
our results yield immediately the corresponding results for
pathwise solutions to stochastic differential equations driven
by such Gaussian process in the sense of rough paths. Moreover,
our LDP result implies the result of Yoshida on the LDP for
capacities over the abstract Wiener space associated with such
Gaussian process.
</p>projecteuclid.org/euclid.ojm/1475601825_20161004132358Tue, 04 Oct 2016 13:23 EDTThe homotopy fixed point sets of spheres actions on rational complexeshttp://projecteuclid.org/euclid.ojm/1475601826<strong>Yanlong Hao</strong>, <strong>Xiugui Liu</strong>, <strong>Qianwen Sun</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 971--981.</p><p><strong>Abstract:</strong><br/>
In this paper, we describe the homotopy type of the homotopy
fixed point sets of $S^{3}$-actions on rational spheres and
complex projective spaces, and provide some properties of
$S^{1}$-actions on a general rational complex.
</p>projecteuclid.org/euclid.ojm/1475601826_20161004132358Tue, 04 Oct 2016 13:23 EDTNotes on quadratic integers and real quadratic number fieldshttp://projecteuclid.org/euclid.ojm/1475601827<strong>Jeongho Park</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 983--1002.</p><p><strong>Abstract:</strong><br/>
It is shown that when a real quadratic integer $\xi$ of fixed
norm $\mu$ is considered, the fundamental unit $\varepsilon_{d}$
of the field $\mathbb{Q}(\xi) = \mathbb{Q}(\sqrt{d})$ satisfies
$\log \varepsilon_{d} \gg (\log d)^{2}$ almost always. An
easy construction of a more general set containing all the
radicands $d$ of such fields is given via quadratic sequences,
and the efficiency of this substitution is estimated explicitly.
When $\mu = -1$, the construction gives all $d$'s for which
the negative Pell's equation $X^{2} - d Y^{2} = -1$ (or more
generally $X^{2} - D Y^{2} = -4$) is soluble. When $\mu$ is
a prime, it gives all of the real quadratic fields in which
the prime ideals lying over $\mu$ are principal.
</p>projecteuclid.org/euclid.ojm/1475601827_20161004132358Tue, 04 Oct 2016 13:23 EDTOne-fixed-point actions on spheres and Smith setshttp://projecteuclid.org/euclid.ojm/1475601828<strong>Masaharu Morimoto</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 1003--1013.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a finite group. The Smith equivalence for real
$G$-modules of finite dimension gives a subset of real representation
ring, called the primary Smith set. Since the primary Smith
set is not additively closed in general, it is an interesting
problem to find a subset which is additively closed in the
real representation ring and occupies a large portion of the
primary Smith set. In this paper we introduce an additively
closed subset of the primary Smith set by means of smooth
one-fixed-point $G$-actions on spheres, and we give evidences
that the subset occupies a large portion of the primary Smith
set if $G$ is an Oliver group.
</p>projecteuclid.org/euclid.ojm/1475601828_20161004132358Tue, 04 Oct 2016 13:23 EDTLie ideal enhancements of counting invariantshttp://projecteuclid.org/euclid.ojm/1475601829<strong>Gillian Roxanne Grindstaff</strong>, <strong>Sam Nelson</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 1015--1027.</p><p><strong>Abstract:</strong><br/>
We define enhancements of the quandle counting invariant for
knots and links with a finite labeling quandle $Q$ embedded
in the quandle of units of a Lie algebra $\mathfrak{a}$ using
Lie ideals. We provide examples demonstrating that the enhancement
is stronger than the associated unenhanced counting invariant
and image enhancement invariant.
</p>projecteuclid.org/euclid.ojm/1475601829_20161004132358Tue, 04 Oct 2016 13:23 EDTSome families of minimal elements for a partial ordering on prime knotshttp://projecteuclid.org/euclid.ojm/1475601830<strong>Fumikazu Nagasato</strong>, <strong>Anh T. Tran</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 1029--1045.</p><p><strong>Abstract:</strong><br/>
We show that all twist knots and certain double twist knots
are minimal elements for a partial ordering on the set of
prime knots. The keys to these results are presentations of
their character varieties using Chebyshev polynomials and
a criterion for irreducibility of a polynomial of two variables.
These give us an elementary method to discuss the number of
irreducible components of the character varieties, which concludes
the result essentially.
</p>projecteuclid.org/euclid.ojm/1475601830_20161004132358Tue, 04 Oct 2016 13:23 EDTConjugacy class and discreteness in $\mathit{SL}(2, \mathbb{C})$http://projecteuclid.org/euclid.ojm/1475601831<strong>Shihai Yang</strong>, <strong>Tiehong Zhao</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 1047--1053.</p><p><strong>Abstract:</strong><br/>
In this note we establish a new discreteness criterion for
a non-elementary group $G$ in $\mathit{SL}(2, \mathbb{C})$. Namely,
$G$ is discrete if all the two-generator subgroups are discrete,
where one generator is a non-trivial element $f$ in $G$, and
the other is in the conjugacy class of $f$.
</p>projecteuclid.org/euclid.ojm/1475601831_20161004132358Tue, 04 Oct 2016 13:23 EDTSome exotic actions of finite groups on smooth 4-manifoldshttp://projecteuclid.org/euclid.ojm/1475601832<strong>Chanyoung Sung</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 1055--1061.</p><p><strong>Abstract:</strong><br/>
Using $G$-monopole invariants, we produce infinitely many
exotic non-free actions of $\mathbb{Z}_{k}\oplus H$ on some
connected sums of finite number of $S^{2}\times S^{2}$, $\mathbb{C}P_{2}$,
$\overline{\mathbb{C}P}_{2}$, and $K3$ surfaces, where $k\geq
2$, and $H$ is any nontrivial finite group acting freely on
$S^{3}$.
</p>projecteuclid.org/euclid.ojm/1475601832_20161004132358Tue, 04 Oct 2016 13:23 EDTOn certain 2-extensions of $\mathbb{Q}$ unramified at 2 and $\infty$http://projecteuclid.org/euclid.ojm/1475601833<strong>Yasushi Mizusawa</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 1063--1088.</p><p><strong>Abstract:</strong><br/>
Based on the method of Boston and Leedham-Green et al. for
computing the Galois groups of tamely ramified $p$-extensions
of number fields, this paper gives a large family of triples
of odd prime numbers such that the maximal totally real $2$-extension
of the rationals unramified outside the three prime numbers
has the Galois group of order $512$ and derived length $3$.
This family is characterized arithmetically, and the explicit
presentation of the Galois group by generators and relations
is also determined completely.
</p>projecteuclid.org/euclid.ojm/1475601833_20161004132358Tue, 04 Oct 2016 13:23 EDTIntegrals on $p$-adic upper half planes and Hida families over totally real fieldshttp://projecteuclid.org/euclid.ojm/1475601834<strong>Isao Ishikawa</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 1089--1124.</p><p><strong>Abstract:</strong><br/>
Bertolini--Darmon and Mok proved a formula of the second derivative
of the two-variable $p$-adic $L$-function of a modular elliptic
curve over a totally real field along the Hida family in terms
of the image of a global point by some $p$-adic logarithm
map. The theory of $p$-adic indefinite integrals and $p$-adic
multiplicative integrals on $p$-adic upper half planes plays
an important role in their work. In this paper, we generalize
these integrals for $p$-adic measures which are not necessarily
$\mathbb{Z}$-valued, and prove a formula of the second derivative
of the two-variable $p$-adic $L$-function of an abelian variety
of $\mathrm{GL}(2)$-type associated to a Hilbert modular form of weight
2.
</p>projecteuclid.org/euclid.ojm/1475601834_20161004132358Tue, 04 Oct 2016 13:23 EDTThe logarithms of Dehn twists on non-orientable surfaceshttp://projecteuclid.org/euclid.ojm/1475601835<strong>Shunsuke Tsuji</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 53, Number 4, 1125--1132.</p><p><strong>Abstract:</strong><br/>
We introduce a Lie algebra associated with a non-orientable
surface, which is an analogue for the Goldman Lie algebra
of an oriented surface. As an application, we deduce an explicit
formula of the Dehn twist along an annulus simple closed curve
on the surface as in Kawazumi--Kuno [4], [5] and Massuyeau--Turaev
[7].
</p>projecteuclid.org/euclid.ojm/1475601835_20161004132358Tue, 04 Oct 2016 13:23 EDTSalem Numbers and Automorphisms of Abelian Surfaceshttp://projecteuclid.org/euclid.ojm/1488531781<strong>Paul Reschke</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 57, Number 1, 1--15.</p><p><strong>Abstract:</strong><br/>
We classify two-dimensional complex tori admitting automorphisms with positive entropy in terms of the entropies they exhibit. For each possible positive value of entropy, we describe the set of two-dimensional complex tori admitting automorphisms with that entropy.
</p>projecteuclid.org/euclid.ojm/1488531781_20170303040403Fri, 03 Mar 2017 04:04 ESTThe normal holonomy of $CR$-submanifoldshttp://projecteuclid.org/euclid.ojm/1488531782<strong>Antonio J. Di Scala</strong>, <strong>Francisco Vittone</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 57, Number 1, 17--35.</p><p><strong>Abstract:</strong><br/>
We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a $CR$-submanifold of a complex space form. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation of a Riemannian symmetric space. In case of a totally real submanifold we give two results about reduction of codimension. We describe explicitly the action of the normal holonomy in the case in which the totally real submanifold is contained in a totally real totally geodesic submanifold. In such a case we prove the compactness of the normal holonomy group.
</p>projecteuclid.org/euclid.ojm/1488531782_20170303040403Fri, 03 Mar 2017 04:04 ESTEffects of Randomization on asymptotic periodicity of nonsingular transformationshttp://projecteuclid.org/euclid.ojm/1488531783<strong>Hiroshi Ishitani</strong>, <strong>Kensuke Ishitani</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 57, Number 1, 37--53.</p><p><strong>Abstract:</strong><br/>
It is known that the Perron--Frobenius operators of piecewise expanding $\mathcal{C}^2$ transformations possess an asymptotic periodicity of densities. On the other hand, external noise or measurement errors are unavoidable in practical systems; therefore, all realistic mathematical models should be regarded as random iterations of transformations. This paper aims to discuss the effects of randomization on the asymptotic periodicity of densities.
</p>projecteuclid.org/euclid.ojm/1488531783_20170303040403Fri, 03 Mar 2017 04:04 ESTPolylogarithmic analogue of the Coleman-Ihara formula, Ihttp://projecteuclid.org/euclid.ojm/1488531784<strong>Hiroaki Nakamura</strong>, <strong>Kenji Sakugawa</strong>, <strong>Zdzisław Wojtkowiak</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 57, Number 1, 55--74.</p><p><strong>Abstract:</strong><br/>
The Coleman-Ihara formula expresses Soule's $p$-adic characters restricted to $p$-local Galois group as the Coates-Wiles homomorphism multiplied by $p$-adic $L$-values at positive integers. In this paper, we show an analogous formula that $\ell$-adic polylogarithmic characters for $\ell=p$ restrict to the Coates-Wiles homomorphism multiplied by Coleman's $p$-adic polylogarithms at any roots of unity of order prime to $p$.
</p>projecteuclid.org/euclid.ojm/1488531784_20170303040403Fri, 03 Mar 2017 04:04 ESTWillmore-like functionals for surfaces in 3-dimensional Thurston geometrieshttp://projecteuclid.org/euclid.ojm/1488531785<strong>Dmitry Berdinsky</strong>, <strong>Yuri Vyatkin</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 57, Number 1, 75--83.</p><p><strong>Abstract:</strong><br/>
We find analogues of the Willmore functional for each of the Thurston geometries with $4$--dimensional isometry group such that the CMC--spheres in these geometries are critical points of these functionals.
</p>projecteuclid.org/euclid.ojm/1488531785_20170303040403Fri, 03 Mar 2017 04:04 ESTRigidity of manifolds with boundary under a lower Ricci curvature boundhttp://projecteuclid.org/euclid.ojm/1488531786<strong>Yohei Sakurai</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 57, Number 1, 85--119.</p><p><strong>Abstract:</strong><br/>
We study Riemannian manifolds with boundary under a lower Ricci curvature bound, and a lower mean curvature bound for the boundary. We prove a volume comparison theorem of Bishop-Gromov type concerning the volumes of the metric neighborhoods of the boundaries. We conclude several rigidity theorems. As one of them, we obtain a volume growth rigidity theorem. We also show a splitting theorem of Cheeger-Gromoll type under the assumption of the existence of a single ray.
</p>projecteuclid.org/euclid.ojm/1488531786_20170303040403Fri, 03 Mar 2017 04:04 ESTComplex structures and non-degenerate closed 2-forms of compact real parallelizable nilmanifoldshttp://projecteuclid.org/euclid.ojm/1488531787<strong>Takumi Yamada</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 57, Number 1, 121--128.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider a relation of non-degenerate closed $2$-forms and complex structures on compact real parallelizable nilmanifolds.
</p>projecteuclid.org/euclid.ojm/1488531787_20170303040403Fri, 03 Mar 2017 04:04 ESTQuadratic approximation in $\mathbb{F}_q(\!(T^{-1})\!)$http://projecteuclid.org/euclid.ojm/1488531788<strong>Tomohiro Ooto</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 57, Number 1, 129--156.</p><p><strong>Abstract:</strong><br/>
In this paper, we study Diophantine exponents $w_n$ and $w_n ^{*}$ for Laurent series over a finite field. Especially, we deal with the case $n=2$, that is, quadratic approximation. We first show that the range of the function $w_2-w_2 ^{*}$ is exactly the closed interval $[0,1]$. Next, we estimate an upper bound of the exponent $w_2$ of continued fractions with low complexity partial quotients.
</p>projecteuclid.org/euclid.ojm/1488531788_20170303040403Fri, 03 Mar 2017 04:04 ESTL'anneau de cohomologie des variétés de Seifert non-orientableshttp://projecteuclid.org/euclid.ojm/1488531789<strong>Anne Bauval</strong>, <strong>Claude Hayat</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 57, Number 1, 157--195.</p><p><strong>Abstract:</strong><br/>
If $p$ is a prime number, the cohomology ring with coefficients in $\mathbb{Z}/p\mathbb{Z}$ of an orientable or non-orientable Seifert manifold $M$ is obtained using a $\Delta$-simplicial decomposition of $M$. Several choices must be made before applying the Alexander-Whitney formula. The answers are given in terms of the classical cellular generators.
</p>projecteuclid.org/euclid.ojm/1488531789_20170303040403Fri, 03 Mar 2017 04:04 ESTMidpoints for Thompson's metric on symmetric coneshttp://projecteuclid.org/euclid.ojm/1488531790<strong>Bas Lemmens</strong>, <strong>Mark Roelands</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 57, Number 1, 197--208.</p><p><strong>Abstract:</strong><br/>
We characterise the affine span of the midpoints sets, $\mathcal{M}(x,y)$, for Thompson's metric on symmetric cones in terms of a translation of the zero-component of the Peirce decomposition of an idempotent. As a consequence we derive an explicit formula for the dimension of the affine span of $\mathcal{M}(x,y)$ in case the associated Euclidean Jordan algebra is simple. In particular, we find for $A$ and $B$ in the cone positive definite Hermitian matrices that \[ \dim({\rm aff}\, \mathcal{M}(A,B))=q^2, \] where $q$ is the number of eigenvalues $\mu$ of $A^{-1}B$, counting multiplicities, such that \[ \mu\neq \max\{\lambda_+(A^{-1}B),\lambda_-(A^{-1}B)^{-1}\}, \] where $\lambda_+(A^{-1}B):=\max \{\lambda\colon \lambda\in\sigma(A^{-1}B)\}$ and $\lambda_-(A^{-1}B):=\min\{\lambda\colon \lambda\in\sigma(A^{-1}B)\}$. These results extend work by Y. Lim [18].
</p>projecteuclid.org/euclid.ojm/1488531790_20170303040403Fri, 03 Mar 2017 04:04 ESTRemark on characterization of wave front set by wave packet transformhttp://projecteuclid.org/euclid.ojm/1496282421<strong>Keiichi Kato</strong>, <strong>Masaharu Kobayashi</strong>, <strong>Shingo Ito</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 209--228.</p><p><strong>Abstract:</strong><br/>
In this paper, we give characterizations of usual wave front set and wave front set in $H^s$ in terms of wave packet transform without any restriction on basic wave packet, which give complete answers of the question raised by G. B. Folland.
</p>projecteuclid.org/euclid.ojm/1496282421_20170531220031Wed, 31 May 2017 22:00 EDTInvariance of an endo-class under the essentially tame Jacquet-Langlands correspondencehttp://projecteuclid.org/euclid.ojm/1496282422<strong>Kazutoshi Kariyama</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 229--247.</p><p><strong>Abstract:</strong><br/>
Let $F$ be a non-Archimedean local field with a finite residue field. We prove that the conjecture, presented by Broussous, Sécherre, and Stevens, is verified in the essetially tame case, that is, that the Jacquet-Langlands correspondence, which was explicitly described by Bushnell and Henniart, preserves an endo-class for irreducible essentially tame representations of inner forms of $\mathrm{GL}_n(F), n \ge 1$, of parametric degree $n$. Moreover we give explicitly a parameter set for such representations of an inner form $G$ of $\mathrm{GL}_n(F)$ which contain simple characters belonging to an endo-class.
</p>projecteuclid.org/euclid.ojm/1496282422_20170531220031Wed, 31 May 2017 22:00 EDTAnalytic extension of Jorge-Meeks type maximal surfaces in Lorentz-Minkowski 3-spacehttp://projecteuclid.org/euclid.ojm/1496282423<strong>Shoichi Fujimori</strong>, <strong>Yu Kawakami</strong>, <strong>Masatoshi Kokubu</strong>, <strong>Wayne Rossman</strong>, <strong>Masaaki Umehara</strong>, <strong>Kotaro Yamada</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 249--272.</p><p><strong>Abstract:</strong><br/>
The Jorge-Meeks $n$-noid ($n\ge 2$) is a complete minimal surface of genus zero with $n$ catenoidal ends in the Euclidean 3-space $\boldsymbol{R}^3$, which has $(2\pi/n)$-rotation symmetry with respect to its axis. In this paper, we show that the corresponding maximal surface $f_n$ in Lorentz-Minkowski 3-space $\boldsymbol{R}^3_1$ has an analytic extension $\tilde f_n$ as a properly embedded zero mean curvature surface. The extension changes type into a time-like (minimal) surface.
</p>projecteuclid.org/euclid.ojm/1496282423_20170531220031Wed, 31 May 2017 22:00 EDTOn the spectral Hausdorff dimension of 1D discrete Schrödinger operators under power decaying perturbationshttp://projecteuclid.org/euclid.ojm/1496282424<strong>V.R. Bazao</strong>, <strong>S.L. Carvalho</strong>, <strong>C.R. de Oliveira</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 273--285.</p><p><strong>Abstract:</strong><br/>
We show that spectral Hausdorff dimensional properties of discrete Schrödinger operators with (1) Sturmian potentials of bounded density and (2) a class of sparse potentials are preserved under suitable polynomial decaying perturbations, when the spectrum of these perturbed operators have some singular continuous component.
</p>projecteuclid.org/euclid.ojm/1496282424_20170531220031Wed, 31 May 2017 22:00 EDTScattering for quasilinear hyperbolic equations of Kirchhoff type with perturbationhttp://projecteuclid.org/euclid.ojm/1496282425<strong>Taeko Yamazaki</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 287--322.</p><p><strong>Abstract:</strong><br/>
This paper is concerned with the abstract quasilinear hyperbolic equations of Kirchhoff type with perturbation. We show the existence of the wave operators and the scattering operator for small data, and that these operators are homeomorphic with respect to a suitable metric in a neighborhood of the origin.
</p>projecteuclid.org/euclid.ojm/1496282425_20170531220031Wed, 31 May 2017 22:00 EDTOn two moduli spaces of sheaves supported on quadric surfaceshttp://projecteuclid.org/euclid.ojm/1496282426<strong>Mario Maican</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 323--333.</p><p><strong>Abstract:</strong><br/>
We show that the moduli space of semi-stable sheaves on a smooth quadric surface, having dimension $1$, multiplicity $4$, Euler characteristic $2$, and first Chern class $(2, 2)$, is the blow-up at two points of a certain hypersurface in a weighted projective space.
</p>projecteuclid.org/euclid.ojm/1496282426_20170531220031Wed, 31 May 2017 22:00 EDTA generalization of Nakai's theorem on locally finite iterative higher derivationshttp://projecteuclid.org/euclid.ojm/1496282427<strong>Shigeru Kuroda</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 335--341.</p><p><strong>Abstract:</strong><br/>
Let $k$ be a field of arbitrary characteristic. In 1978, Nakai proved a structure theorem for $k$-domains admitting a nontrivial locally finite iterative higher derivation when $k$ is algebraically closed. In this paper, we generalize Nakai's theorem to cover the case where $k$ is not algebraically closed. As a consequence, we obtain a cancellation theorem of the following form: Let $A$ and $A'$ be finitely generated $k$-domains with $A[x]\simeq _kA'[x]$. If $A$ and $\bar{k}\otimes _kA$ are UFDs and $\mathop{\rm trans.deg}\nolimits _kA=2$, then we have $A\simeq _kA'$. This generalizes the cancellation theorem of Crachiola.
</p>projecteuclid.org/euclid.ojm/1496282427_20170531220031Wed, 31 May 2017 22:00 EDT$p$-local stable cohomological rigidity of quasitoric manifoldshttp://projecteuclid.org/euclid.ojm/1496282428<strong>Sho Hasui</strong>, <strong>Daisuke Kishimoto</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 343--350.</p><p><strong>Abstract:</strong><br/>
It is proved that if two quasitoric manifolds of dimension $\le 2p^2-4$ for a prime $p$ have isomorphic cohomology rings, then they have the same $p$-local stable homotopy type.
</p>projecteuclid.org/euclid.ojm/1496282428_20170531220031Wed, 31 May 2017 22:00 EDTFree product of two elliptic quaternionic Möbius transformationshttp://projecteuclid.org/euclid.ojm/1496282429<strong>Wensheng Cao</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 351--362.</p><p><strong>Abstract:</strong><br/>
Suppose that $f$ and $g$ are two elliptic quaternionic Möbius transformations of orders $m$ and $n$ respectively. If the hyperbolic distance $\delta(f,g)$ between ${\rm fix}(f)$ and ${\rm fix}(g)$ satisfies $$\cosh \delta(f,g) \geq\frac{\cos\frac{\pi}{m}\cos\frac{\pi}{n}+1}{\sin\frac{\pi}{m}\sin\frac{\pi}{n}},$$ then the group $\langle f , g\rangle$ is discrete non-elementary and isomorphic to the free product $\langle f \rangle* \langle g\rangle$.
</p>projecteuclid.org/euclid.ojm/1496282429_20170531220031Wed, 31 May 2017 22:00 EDTPretzel Knots and $q$-Serieshttp://projecteuclid.org/euclid.ojm/1496282430<strong>Mohamed Elhamdadi</strong>, <strong>Mustafa Hajij</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 363--381.</p><p><strong>Abstract:</strong><br/>
The tail of the colored Jones polynomial of an alternating link is a $q$-series invariant whose first $n$ terms coincide with the first $n$ terms of the $n$-th colored Jones polynomial. Recently, it has been shown that the tail of the colored Jones polynomial of torus knots give rise to Ramanujan type identities. In this paper, we study $q$-series identities coming from the colored Jones polynomial of pretzel knots. We prove a false theta function identity that goes back to Ramanujan and we give a natural generalization of this identity using the tail of the colored Jones polynomial of Pretzel knots. Furthermore, we compute the tail for an infinite family of Pretzel knots and relate it to false theta function-type identities.
</p>projecteuclid.org/euclid.ojm/1496282430_20170531220031Wed, 31 May 2017 22:00 EDTOn the Gevrey strong hyperbolicityhttp://projecteuclid.org/euclid.ojm/1496282431<strong>Tatsuo Nishitani</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 383--408.</p><p><strong>Abstract:</strong><br/>
In this paper we are concerned with a homogeneous differential operator $p$ of order $m$ of which characteristic set of order $m$ is assumed to be a smooth manifold. We define the Gevrey strong hyperbolicity index as the largest number $s$ such that the Cauchy problem for $p+Q$ is well-posed in the Gevrey class of order $s$ for any differential operator $Q$ of order less than $m$. We study the case of the largest index and we discuss in which way the Gevrey strong hyperbolicity index relates with the geometry of bicharacteristics of $p$ near the characteristic manifold.
</p>projecteuclid.org/euclid.ojm/1496282431_20170531220031Wed, 31 May 2017 22:00 EDTMori Dream Spaces extremal contractions of K3 surfaceshttp://projecteuclid.org/euclid.ojm/1502092821<strong>Alice Garbagnati</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 409--433.</p><p><strong>Abstract:</strong><br/>
We will give a criterion to assure that an extremal contraction of a K3 surface which is not a Mori Dream Space produces a singular surface which is a Mori Dream Space. We list the possible Néron--Severi groups of K3 surfaces with this property and an extra geometric condition such that the Picard number is greater than or equal to 10. We give a detailed description of two geometric examples for which the Picard number of the K3 surface is 3, i.e. the minimal possible in order to have the required property. Moreover we observe that there are infinitely many examples of K3 surfaces with the required property and Picard number equal to 3.
</p>projecteuclid.org/euclid.ojm/1502092821_20170807040038Mon, 07 Aug 2017 04:00 EDTWeak convergence of regular Dirichlet subspaceshttp://projecteuclid.org/euclid.ojm/1502092822<strong>Liping Li*</strong>, <strong>Toshihiro Uemura</strong>, <strong>Jiangang Ying**</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 435--455.</p><p><strong>Abstract:</strong><br/>
In this paper we shall prove the weak convergence of the associated diffusion processes of regular subspaces with monotone characteristic sets for a fixed Dirichlet form. More precisely, given a fixed 1-dimensional diffusion process and a sequence of its regular subspaces, if the characteristic sets of regular subspaces are decreasing or increasing, then their associated diffusion processes are weakly convergent to another diffusion process. This is an extended result of [14].
</p>projecteuclid.org/euclid.ojm/1502092822_20170807040038Mon, 07 Aug 2017 04:00 EDTA finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surfacehttp://projecteuclid.org/euclid.ojm/1502092823<strong>Ryoma Kobayashi</strong>, <strong>Genki Omori</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 457--474.</p><p><strong>Abstract:</strong><br/>
We obtain a finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface. The generating set consists of crosscap pushing maps along non-separating two-sided simple loops and squares of Dehn twists along non-separating two-sided simple closed curves. We also prove that the level 2 twist subgroup is normally generated in the mapping class group by a crosscap pushing map along a non-separating two-sided simple loop for genus $g\geq 5$ and $g=3$. As an application, we calculate the first homology group of the level 2 twist subgroup for genus $g\geq 5$ and $g=3$.
</p>projecteuclid.org/euclid.ojm/1502092823_20170807040038Mon, 07 Aug 2017 04:00 EDTCritical levels and Jacobi fields in a complex of cycleshttp://projecteuclid.org/euclid.ojm/1502092824<strong>Ingrid Irmer</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 475--497.</p><p><strong>Abstract:</strong><br/>
In this paper it is shown that the space of tight geodesic segments connecting any two vertices in a complex of cycles has finite, uniformly bounded dimension. The dimension is defined in terms of a discrete analogue of Jacobi fields, which are explicitly constructed and shown to give a complete description of the entire space of tight geodesics. Jacobi fields measure the extent to which geodesic stability breaks down. Unlike most finiteness properties of curve complexes, the arguments presented here do not rely on hyperbolicity, but rather on structures similar to Morse theory.
</p>projecteuclid.org/euclid.ojm/1502092824_20170807040038Mon, 07 Aug 2017 04:00 EDTFeller evolution families and parabolic equations with form-bounded vector fieldshttp://projecteuclid.org/euclid.ojm/1502092825<strong>Damir Kinzebulatov</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 499--516.</p><p><strong>Abstract:</strong><br/>
We show that the weak solutions of parabolic equation $\partial_t u - \Delta u + b(t,x) \cdot \nabla u=0$, $(t,x) \in (0,\infty) \times \mathbb R^d$, $d \geqslant 3$, for $b(t,x)$ in a wide class of time-dependent vector fields capturing critical order singularities, constitute a Feller evolution family and, thus, determine a Feller process. Our proof uses an a priori estimate on the $L^p$-norm of the gradient of solution in terms of the $L^q$-norm of the gradient of initial function, and an iterative procedure that moves the problem of convergence in $L^\infty$ to $L^p$.
</p>projecteuclid.org/euclid.ojm/1502092825_20170807040038Mon, 07 Aug 2017 04:00 EDTCompactness of Markov and Schrödinger semi-groups: A probabilistic approachhttp://projecteuclid.org/euclid.ojm/1502092826<strong>Masayoshi Takeda</strong>, <strong>Yoshihiro Tawara</strong>, <strong>Kaneharu Tsuchida</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 517--532.</p><p><strong>Abstract:</strong><br/>
It is proved if an irreducible, strong Feller symmetric Markov process possesses a tightness property, then its semi-group is an $L^2$-compact operator. In this paper, applying this fact, we prove probabilistically the compactness of Dirichlet-Laplacians and Schrödinger operators.
</p>projecteuclid.org/euclid.ojm/1502092826_20170807040038Mon, 07 Aug 2017 04:00 EDTLie algebras constructed with Lie modules and their positively and negatively graded moduleshttp://projecteuclid.org/euclid.ojm/1502092827<strong>Nagatoshi Sasano</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 533--568.</p><p><strong>Abstract:</strong><br/>
In this paper, we shall give a way to construct a graded Lie algebra $L(\mathfrak{g},\rho,V,{\cal V},B_0)$ from a standard pentad $(\mathfrak{g},\rho,V,{\cal V},B_0)$ which consists of a Lie algebra $\mathfrak{g}$ which has a non-degenerate invariant bilinear form $B_0$ and $\mathfrak{g}$-modules $(\rho, V)$ and ${\cal V}\subset \mathrm {Hom }(V,F)$ all defined over a field $F$ with characteristic $0$. In general, we do not assume that these objects are finite-dimensional. We can embed the objects $\mathfrak{g},\rho,V,{\cal V}$ into $L(\mathfrak{g},\rho,V,{\cal V},B_0)$. Moreover, we construct specific positively and negatively graded modules of $L(\mathfrak{g},\rho,V,{\cal V},B_0)$. Finally, we give a chain rule on the embedding rules of standard pentads.
</p>projecteuclid.org/euclid.ojm/1502092827_20170807040038Mon, 07 Aug 2017 04:00 EDTOn Jacobi forms of real weights and indiceshttp://projecteuclid.org/euclid.ojm/1502092828<strong>Hiroki Aoki</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 569--585.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate weak Jacobi forms of real weights and indices, and show that they have a very simple structure theorem even when their weights and indices are not integral. By using this structure theorem, we can determine possible weights of Siegel paramodular forms.
</p>projecteuclid.org/euclid.ojm/1502092828_20170807040038Mon, 07 Aug 2017 04:00 EDTA twisted first homology group of the handlebody mapping class grouphttp://projecteuclid.org/euclid.ojm/1502092829<strong>Tomohiko Ishida</strong>, <strong>Masatoshi Sato</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 587--619.</p><p><strong>Abstract:</strong><br/>
Let $H_g$ be a 3-dimensional handlebody of genus $g$. We determine the twisted first homology group of the mapping class group of $H_g$ with coefficients in the first integral homology group of the boundary surface $\partial H_g$ for $g\ge2$.
</p>projecteuclid.org/euclid.ojm/1502092829_20170807040038Mon, 07 Aug 2017 04:00 EDTCorrigendum to ``Deformations of special Legendrian submanifolds with boundary" Osaka J. Math. 51 (2014), 673--693http://projecteuclid.org/euclid.ojm/1502092830<strong>Guangcun Lu</strong>, <strong>Xiaomin Chen</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 621--622.</p><p><strong>Abstract:</strong><br/>
</p>projecteuclid.org/euclid.ojm/1502092830_20170807040038Mon, 07 Aug 2017 04:00 EDT