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

Brown, Brian Malcolm and Marletta, Marco and 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. ISSN 0024-6107. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/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.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Ian Wood
Date Deposited: 09 Apr 2010 10:58
Last Modified: 10 Dec 2014 18:16
Resource URI: https://kar.kent.ac.uk/id/eprint/23939 (The current URI for this page, for reference purposes)
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