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

D. Burghelea, Leonid Friedlander, T. Kappeler

Research output: Contribution to journalArticle

41 Citations (Scopus)

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
StatePublished - May 1991
Externally publishedYes

Fingerprint

Difference Operator
Vector Bundle
determinants
bundles
Finite Difference
Determinant
operators
Difference Approximation
differential operators
Monodromy
Elliptic Operator
Differential operator
Signature
signatures
Angle
Invariant
approximation

ASJC Scopus subject areas

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

Cite this

On the determination of elliptic differential and finite difference operators in vector bundles over S1. / Burghelea, D.; Friedlander, Leonid; Kappeler, T.

In: Communications in Mathematical Physics, Vol. 138, No. 1, 05.1991, p. 1-18.

Research output: Contribution to journalArticle

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