Brown, B.M. and Marletta, M. and Naboko, S. and Wood, I. (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.
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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.
|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:||06 Jan 2012 15:25|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/23939 (The current URI for this page, for reference purposes)|
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