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An extension of the work of V. Guillemin on complex powers and zeta functions of elliptic pseudodifferential operators
Author(s):
Bogdan
Bucicovschi
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3081-3090.
MSC (1991):
Primary 58G25, 35P05
Posted:
April 23, 1999
MathSciNet review:
1605924
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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:
- [BFKM]
- D. Burghelea, L. Friedlander, T. Kappeler, P. MacDonald, Analytic and Reidemeister Torsion for Representations in Finite Type Hilbert Modules, Geometric and Functional Analysis 6 (5) (1996), 752-859. MR 97i:58177
- [G]
- V. Guillemin, A New Proof of Weyl's Formula on the Asymptotic Distribution of Eigenvalues, Adv. in Math. 55 (1985), 131-160. MR 86i:58135
- [Gi]
- P. Gilkey, Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem, Publish or Perish, Wilmington, (1984). MR 86j:58144
- [RS]
- M. Reed, B. Simon, Methods of Modern Mathematical Physics, Functional Analysis I, Academic Press, Revised and Enlarged Edition, (1980). MR 85e:46002
- [S]
- R. Seeley, Complex Powers of an Elliptic Operator, Proc. Symp. Pure Math. AMS 10 (1967), 288-307. MR 38:6220
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Additional Information:
Bogdan
Bucicovschi
Affiliation:
Department of Mathematics, Ohio State University, 231 W 18th Ave., Columbus, Ohio 43210
Email:
bogdanb@math.ohio-state.edu
DOI:
10.1090/S0002-9939-99-04867-4
PII:
S 0002-9939(99)04867-4
Received by editor(s):
December 1, 1997
Posted:
April 23, 1999
Communicated by:
Peter Li
Copyright of article:
Copyright
1999,
American Mathematical Society
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