Regularized determinants for pseudodifferential operators in vector bundles over S1

D. Burghelea, Leonid Friedlander, T. Kappeler

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 to A, 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.

Original languageEnglish (US)
Pages (from-to)496-513
Number of pages18
JournalIntegral Equations and Operator Theory
Volume16
Issue number4
DOIs
StatePublished - Dec 1993

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Pseudodifferential Operators
Vector Bundle
Determinant
Elliptic Operator
Invertible
Fredholm Determinant
Invariant
Operator
Explicit Formula
Express

Keywords

  • MSC1991: Primary 34L05, Secondary 35S05

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

Cite this

Regularized determinants for pseudodifferential operators in vector bundles over S1 . / Burghelea, D.; Friedlander, Leonid; Kappeler, T.

In: Integral Equations and Operator Theory, Vol. 16, No. 4, 12.1993, p. 496-513.

Research output: Contribution to journalArticle

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