On the determination of elliptic differential and finite difference operators in vector bundles over S1

D. Burghelea, Leonid Friedlander, T. Kappeler

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Abstract

For an elliptic differential operator A over S1, {Mathematical expression}, with Ak(x) in END(ℂr) and θ as a principal angle, the ζ-regularized determinant DetθA is computed in terms of the monodromy map PA, associated to A and some invariant expressed in terms of An and An-1. A similar formula holds for finite difference operators. A number of applications and implications are given. In particular we present a formula for the signature of A when A is self adjoint and show that the determinant of A is the limit of a sequence of computable expressions involving determinants of difference approximation of A.

Original languageEnglish (US)
Pages (from-to)1-18
Number of pages18
JournalCommunications in Mathematical Physics
Volume138
Issue number1
DOIs
Publication statusPublished - May 1991
Externally publishedYes

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

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