Jump to ContentJump to Main Navigation
Traces and Determinants of Pseudodifferential Operators$
Users without a subscription are not able to see the full content.

Simon Scott

Print publication date: 2010

Print ISBN-13: 9780198568360

Published to Oxford Scholarship Online: January 2011

DOI: 10.1093/acprof:oso/9780198568360.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 21 July 2019

Pseudodifferential Operator Trace Formulae

Pseudodifferential Operator Trace Formulae

Chapter:
(p.407) IV. Pseudodifferential Operator Trace Formulae
Source:
Traces and Determinants of Pseudodifferential Operators
Author(s):

Simon Scott

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198568360.003.0005

In this chapter details of the construction of the fundamental trace functionals on pseudodifferential operators are given. The approach to traces taken here is through an analysis of the singularity structure of the operator Schwartz kernel. This allows for a dual perspective on traces, viewed either from the microanalytic approach of pseudodifferential methods or from the approach favoured in applications in geometric analysis, differential geometry, and theoretical physics, of subtracting-off the singular part of the kernel. Regularized traces arise via subtracting-off from the Schwartz kernel the meromorphic continuation of homogeneous distributions defined by the pseudodifferential operator symbol, linking trace regularization methods with traditional distributional analysis. Exact formulae are computed for regularized trace functionals for log-classical pseudodifferential operators, allowing, in particular, precise formulae for the zeta determinant. The final part of the chapter analyses the principal multiplicative functional on the semiqroup of pseudodifferential operators.

Keywords:   Distributions, homogeneous, Schwartz kernel, singularity structure, extended trace, residue trace, log-classical, log polyhomogeneous symbols, residue determinant, proofs, construction quasi-trace, trace defect formulae

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .