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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| 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: | 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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