Determinants of zeroth order operators

Leonid Friedlander, Victor Guillemin

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

For compact Riemannian manifolds all of whose geodesics are closed (aka Zoll manifolds) one can define the determinant of a zeroth order pseudodifferential operator by mimicking Szego’s definition of this determinant for the operator: multiplication by a bounded function, on the Hilbert space of square-integrable functions on the circle. In this paper we prove that the non-local contribution to this determinant can be computed in terms of a much simpler “zeta-regularized” determinant.

Original languageEnglish (US)
Pages (from-to)1-12
Number of pages12
JournalJournal of Differential Geometry
Volume78
Issue number1
DOIs
StatePublished - Jan 1 2008

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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