Scattering Theory, the Adiabatic Decomposition of the Ζ-determinant and the Dirichlet to Neumann Operator
نویسنده
چکیده
We also discuss the relation of our work to the earlier work on the decomposition of the ζ-determinant by Burghelea, Friedlander and Kappeler (from this point on referred to as BFK). The present work is companion to the paper [10] and in several places we refer to [10] for the proof of a given statement and a more detailed discussion. Let D : C(M ;S) → C(M ;S) be a compatible Dirac operator acting on sections of a bundle of Clifford modules S over a closed manifold M . The operator D is a self-adjoint operator with discrete spectrum. We also assume that we have a decomposition of M as M1 ∪M2 where M1 and M2 are compact manifolds with boundaries such that
منابع مشابه
Adiabatic Decomposition of the Ζ-determinant and Dirichlet to Neumann Operator
Abstract. This paper is companion to our earlier work [8] (see also announcement [7]). Let M be a closed manifold and Y be an embedded hypersurface, such that there is a decomposition of M = M1 ∪M2 into two manifolds with boundary M1 and M2 , with M1 ∩M2 = Y . In [8] we proved the decomposition formula for detζ∆ the ζ-determinant of a Dirac Laplacian ∆ on M . The contributions coming from M1 an...
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