Duke Mathematical Journal

The multiplicative anomaly for determinants of elliptic operators

Kate Okikiolu
Source: Duke Math. J. Volume 79, Number 3 (1995), 723-750.
First Page: Show Hide
Primary Subjects: 58G26
Secondary Subjects: 47G30, 58G15
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077285355
Mathematical Reviews number (MathSciNet): MR1355182
Zentralblatt MATH identifier: 0851.58048
Digital Object Identifier: doi:10.1215/S0012-7094-95-07919-8

References

[1] D. Burghelea, L. Friedlander, and T. Kappeler, On the determinant of elliptic differential and finite difference operators in vector bundles over $S^1$, Comm. Math. Phys. 138 (1991), no. 1, 1–18.
Mathematical Reviews (MathSciNet): MR92f:58193
Zentralblatt MATH: 0734.58043
Digital Object Identifier: doi:10.1007/BF02099666
Project Euclid: euclid.cmp/1104202844
[2] T. Branson and B. Ørsted, Conformal geometry and global invariants, Differential Geom. Appl. 1 (1991), no. 3, 279–308.
Mathematical Reviews (MathSciNet): MR94k:58154
Zentralblatt MATH: 0785.53025
Digital Object Identifier: doi:10.1016/0926-2245(91)90004-S
[3] T. Branson and B. Ørsted, Explicit functional determinants in four dimensions, Proc. Amer. Math. Soc. 113 (1991), no. 3, 669–682.
Mathematical Reviews (MathSciNet): MR92b:58238
Zentralblatt MATH: 0762.47019
Digital Object Identifier: doi:10.2307/2048601
[4] T. Branson, S. Y. A. Chang, and P. Yang, Estimates and extremals for zeta function determinants on four-manifolds, Comm. Math. Phys. 149 (1992), no. 2, 241–262.
Mathematical Reviews (MathSciNet): MR93m:58116
Zentralblatt MATH: 0761.58053
Digital Object Identifier: doi:10.1007/BF02097624
Project Euclid: euclid.cmp/1104251221
[5] S. Y. A. Chang and P. Yang, Extremal metrices of zeta function determinants on $4$-manifolds, to appear in Annals of Math.
Mathematical Reviews (MathSciNet): MR1338677
Zentralblatt MATH: 0842.58011
Digital Object Identifier: doi:10.2307/2118613
[6] L. Friedlander, Determinants of Elliptic Operators, Thesis, Massachusetts Institute of Technology, 1989.
[7] S. Fulling and G. Kennedy, The resolvent parametrix of the general elliptic linear differential operator: a closed form for the intrinsic symbol, Trans. Amer. Math. Soc. 310 (1988), no. 2, 583–617.
Mathematical Reviews (MathSciNet): MR90b:58260
Zentralblatt MATH: 0711.35155
Digital Object Identifier: doi:10.2307/2000982
[8] V. Guillemin, A new proof of Weyl's formula on the asymptotic distribution of eigenvalues, Adv. in Math. 55 (1985), no. 2, 131–160.
Mathematical Reviews (MathSciNet): MR86i:58135
Zentralblatt MATH: 0559.58025
Digital Object Identifier: doi:10.1016/0001-8708(85)90018-0
[9] L. Hörmander, The Analysis of Linear Partial Differential Operators III, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 274, Springer-Verlag, Berlin, 1985.
Mathematical Reviews (MathSciNet): MR87d:35002a
Zentralblatt MATH: 0601.35001
[10] M. Kontseivick and S. Vishik, Determinants of elliptic pseudodifferential operators, preprint, 1994.
[11] I. Gohberg and M. Kreĭ n, Introduction to the theory of linear nonselfadjoint operators, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969.
Mathematical Reviews (MathSciNet): MR39:7447
Zentralblatt MATH: 0181.13504
[12] K. Okikiolu, The Campbell-Hausdorff theorem for elliptic operators and a related trace formula, Duke Math. J. 79 (1995), no. 3, 687–722.
Mathematical Reviews (MathSciNet): MR96j:58175
Zentralblatt MATH: 0854.35137
Digital Object Identifier: doi:10.1215/S0012-7094-95-07918-6
Project Euclid: euclid.dmj/1077285354
[13] A. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B 103 (1981), no. 3, 207–210.
Mathematical Reviews (MathSciNet): MR84h:81093a
Digital Object Identifier: doi:10.1016/0370-2693(81)90743-7
[14] A. Polyakov, Quantum geometry of Fermionic strings, Phys. Lett. B 103 (1981), no. 3, 211–213.
Mathematical Reviews (MathSciNet): MR84h:81093b
Digital Object Identifier: doi:10.1016/0370-2693(81)90744-9
[15] D. Ray and I. Singer, $R$-torsion and the Laplacian on Riemannian manifolds, Advances in Math. 7 (1971), 145–210.
Mathematical Reviews (MathSciNet): MR45:4447
Zentralblatt MATH: 0239.58014
Digital Object Identifier: doi:10.1016/0001-8708(71)90045-4
[16] V. Romanov and A. Schwartz, Anomalies and elliptic operators, Theor. and Math. Phys. 416 (1979), 190–204 (Russian).
[17] B. Osgood, R. Phillips, and P. Sarnak, Extremals of determinants of Laplacians, J. Funct. Anal. 80 (1988), no. 1, 148–211.
Mathematical Reviews (MathSciNet): MR90d:58159
Zentralblatt MATH: 0653.53022
Digital Object Identifier: doi:10.1016/0022-1236(88)90070-5
[18] R. Seeley, Complex powers of an elliptic operator, Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966), Proc. Sympos. Pure Math., vol. 10, Amer. Math. Soc., Providence, R.I., 1967, pp. 288–307.
Mathematical Reviews (MathSciNet): MR38:6220
Zentralblatt MATH: 0159.15504
[19] R. Strichartz, A functional calculus for elliptic pseudodifferential operators, Amer. J. Math. 94 (1972), 711–722.
Mathematical Reviews (MathSciNet): MR46:9811
Zentralblatt MATH: 0246.35082
Digital Object Identifier: doi:10.2307/2373753
[20] F. Treves, Introduction to pseudodifferential and Fourier integral operators. Vol. 1, Plenum Press, New York, 1980.
Mathematical Reviews (MathSciNet): MR82i:35173
Zentralblatt MATH: 0453.47027
[21] M. Wodzicki, Non-commutative residue, Chapter I. Fundamentals, $K$-Theory, Arithmetic, and Geometry (Moscow, 1984–1986), Lecture Notes in Math, vol. 1289, Springer-Verlag, Berlin, 1987, pp. 320–399.
Mathematical Reviews (MathSciNet): MR90a:58175
Zentralblatt MATH: 0649.58033
Digital Object Identifier: doi:10.1007/BFb0078372

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?