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

Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Marletta, Marco ORCID: https://orcid.org/0000-0003-1546-4046, Naboko, Serguei and Wood, Ian 2008. Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices. Journal of the London Mathematical Society 77 (3) , pp. 700-718. 10.1112/jlms/jdn006

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics Computer Science & Informatics
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Publisher:	London Mathematical Society
ISSN:	0024-6107
Last Modified:	18 Oct 2022 12:42
URI:	https://orca.cardiff.ac.uk/id/eprint/10967

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