Boundary triplets and M -functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices

2008/03/20 by Malcolm Brown, Marco Marletta, Serguei Naboko +1 · 1 citation
Mathematics · #Spectral Theory in Mathematical Physics #Holomorphic and Operator Theory #Differential Equations and Boundary Problems

paper · doi:10.1112/jlms/jdn006

Abstract

Starting with an adjoint pair of operators, under suitable abstract versions of standard PDE hypotheses, we consider the Weyl M-function of extensions of the operators. The extensions are determined by abstract boundary conditions and we establish results on the relationship between the M-function as an analytic function of a spectral parameter and the spectrum of the extension. We also give an example where the M-function does not contain the whole spectral information of the resolvent, and show that the results can be applied to elliptic PDEs where the M-function corresponds to the Dirichlet to Neumann map.

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• Generalized boundary triples for adjoint pairs with applications to non-self-adjoint Schrödinger operators

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