An Extension of the Work of V. Guillemin on Complex Powers and Zeta Functions of Elliptic Pseudodifferential Operators

1997/05/09 by Bogdan Bucicovschi, Bucicovschi, Bogdan
Mathematics · #Differential Equations and Boundary Problems #Differential Geometry (math.DG) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9705006

11 pages, AMS-Tex, Minor Corrections

openalex publication_date 1997/05/09 · arxiv created 1997/05/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this note is to extend the results of V. 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 of Hilbert modules of finite type over a finite von Neumann algebra.

Related

• Complex powers and non-compact manifolds
• Seeley's Theory of Pseudodifferential Operators on Orbifolds
• Pseudodifferential Operators on Q_p and L-Series
• Elliptic systems of variable order
• The local and global parts of the basic zeta coefficient for operators on manifolds with boundary