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

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

2007-04-19

arxiv.org/abs/0704.2562v3

Mathematics

Spectral Theory

16 pages, submitted to LMS; v2: including more references and some minor corrections; changed presentation in section 2, added

Scientific paper

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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