Meyer-vietoris type formula for determinants of elliptic differential operators

D. Burghelea, Leonid Friedlander, T. Kappeler

Research output: Contribution to journalArticle

74 Citations (Scopus)

Abstract

For a closed codimension one submanifold Γ of a compact manifold M, let MΓ be the manifold with boundary obtained by cutting M along Γ. Let A be an elliptic differential operator on M and B and C be two complementary boundary conditions on Γ. If (A, B) is an elliptic boundary valued problem on MΓ, then one defines an elliptic pseudodifferential operator R of Neumann type on Γ and prove the following factorization formula for the ζ-regularized determinants: DetA Det(A, B) = KDetR, with K a local quantity depending only on the jets of the symbols of A, B and C along Γ. The particular case when M has dimension 2, A is the Laplace-Beltrami operator, and B resp. C is the Dirichlet resp. Neumann boundary condition is considered.

Original languageEnglish (US)
Pages (from-to)34-65
Number of pages32
JournalJournal of Functional Analysis
Volume107
Issue number1
DOIs
StatePublished - 1992
Externally publishedYes

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Elliptic Operator
Differential operator
Determinant
Sum formula
Laplace-Beltrami Operator
Manifolds with Boundary
Pseudodifferential Operators
Neumann Boundary Conditions
Compact Manifold
Submanifolds
Codimension
Dirichlet
Boundary conditions
Closed

ASJC Scopus subject areas

  • Analysis

Cite this

Meyer-vietoris type formula for determinants of elliptic differential operators. / Burghelea, D.; Friedlander, Leonid; Kappeler, T.

In: Journal of Functional Analysis, Vol. 107, No. 1, 1992, p. 34-65.

Research output: Contribution to journalArticle

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