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Regularized determinants for pseudodifferential operators in vector bundles over S¹


Burghelea, D; Friedlander, L; Kappeler, T (1993). Regularized determinants for pseudodifferential operators in vector bundles over S¹. Integral Equations Operator Theory, 16(4):496-513.

Abstract

We express the ζ-regularized determinant of an elliptic pseudodifferential operator A over S¹ with strongly invertible principal symbol in terms of the Fredholm determinant of an operator of determinant class, canonically associated toA, and local invariants. These invariants are given by explicit formulae involving the principal and subprincipal symbol of the operator. We remark that,generically, elliptic pseudodifferential operators have a strongly invertible principal symbol.

Abstract

We express the ζ-regularized determinant of an elliptic pseudodifferential operator A over S¹ with strongly invertible principal symbol in terms of the Fredholm determinant of an operator of determinant class, canonically associated toA, and local invariants. These invariants are given by explicit formulae involving the principal and subprincipal symbol of the operator. We remark that,generically, elliptic pseudodifferential operators have a strongly invertible principal symbol.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1993
Deposited On:29 Nov 2010 16:29
Last Modified:05 Apr 2016 13:28
Publisher:Birkhäuser
ISSN:0378-620X
Publisher DOI:https://doi.org/10.1007/BF01205290
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1216460
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0784.35126

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