Determinants of zeroth order operators

Leonid Friedlander, Victor Guillemin

Research output: Contribution to journalArticle

3 Citations (Scopus)

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
StatePublished - Jan 2008

Fingerprint

Zeroth
Determinant
Operator
Multiplication Operator
Pseudodifferential Operators
Compact Manifold
Geodesic
Riemannian Manifold
Circle
Hilbert space
Closed

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

Cite this

Determinants of zeroth order operators. / Friedlander, Leonid; Guillemin, Victor.

In: Journal of Differential Geometry, Vol. 78, No. 1, 01.2008, p. 1-12.

Research output: Contribution to journalArticle

Friedlander, Leonid ; Guillemin, Victor. / Determinants of zeroth order operators. In: Journal of Differential Geometry. 2008 ; Vol. 78, No. 1. pp. 1-12.
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