An extension of the work of V. Guillemin on complex powers and zeta functions of elliptic pseudodifferential operators

Bucicovschi, Bogdan

doi:10.1090/S0002-9939-99-04867-4

An extension of the work of V. Guillemin on complex powers and zeta functions of elliptic pseudodifferential operators
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Proc. Amer. Math. Soc. 127 (1999), 3081-3090 Request permission

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.

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