An extension of the work of V. Guillemin on complex powers and zeta functions of elliptic pseudodifferential operators
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- by Bogdan Bucicovschi
- Proc. Amer. Math. Soc. 127 (1999), 3081-3090
- DOI: https://doi.org/10.1090/S0002-9939-99-04867-4
- Published electronically: April 23, 1999
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Abstract:
The purpose of this note is to extend the methods and results of Guillemin on elliptic self-adjoint pseudodifferential operators of order one, from operators defined on smooth functions on a closed manifold to operators defined on smooth sections in a vector bundle. The case of bundles of Hilbert modules of finite type over a finite von Neumann algebra will also be treated.References
- D. Burghelea, L. Friedlander, T. Kappeler, and P. McDonald, Analytic and Reidemeister torsion for representations in finite type Hilbert modules, Geom. Funct. Anal. 6 (1996), no. 5, 751–859. MR 1415762, DOI 10.1007/BF02246786
- Victor Guillemin, A new proof of Weyl’s formula on the asymptotic distribution of eigenvalues, Adv. in Math. 55 (1985), no. 2, 131–160. MR 772612, DOI 10.1016/0001-8708(85)90018-0
- Peter B. Gilkey, Invariance theory, the heat equation, and the Atiyah-Singer index theorem, Mathematics Lecture Series, vol. 11, Publish or Perish, Inc., Wilmington, DE, 1984. MR 783634
- Michael Reed and Barry Simon, Methods of modern mathematical physics. I, 2nd ed., Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. Functional analysis. MR 751959
- R. T. Seeley, Complex powers of an elliptic operator, Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966) Amer. Math. Soc., Providence, R.I., 1967, pp. 288–307. MR 0237943
Bibliographic Information
- Bogdan Bucicovschi
- Affiliation: Department of Mathematics, Ohio State University, 231 W 18th Ave., Columbus, Ohio 43210
- Email: bogdanb@math.ohio-state.edu
- Received by editor(s): December 1, 1997
- Published electronically: April 23, 1999
- Communicated by: Peter Li
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3081-3090
- MSC (1991): Primary 58G25, 35P05
- DOI: https://doi.org/10.1090/S0002-9939-99-04867-4
- MathSciNet review: 1605924