BOUNDARY TRIPLETS AND M-FUNCTIONS FOR NON-SELFADJOINT OPERATORS, WITH APPLICATIONS TO ELLIPTIC PDES AND BLOCK OPERATOR MATRICES

Brown, Malcolm S. and Marletta, Marco and Naboko, Serguei and Wood, Ian Geoffrey (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 available from this repository)

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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: 13 May 2014 12:50
Resource URI: http://kar.kent.ac.uk/id/eprint/23939 (The current URI for this page, for reference purposes)
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