Brown, B.M. and Hinchcliffe, J. and Marletta, M. and Naboko, S. and Wood, I. (2009) THE ABSTRACT TITCHMARSH-WEYL M-FUNCTION FOR ADJOINT OPERATOR PAIRS AND ITS RELATION TO THE SPECTRUM. Integral Equations and Operator Theory, 63 (3). pp. 297-320. ISSN 0378-620X.
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| Official URL http://dx.doi.org/10.1007/s00020-009-1668-z |
Abstract
In the setting of adjoint pairs of operators we consider the question: to what extent does the Weyl M-function see the same singularities as the resolvent of a certain restriction AB of the maximal operator? We obtain results showing that it is possible to describe explicitly certain spaces S and S such that the resolvent bordered by projections onto these subspaces is analytic everywhere that the M-function is analytic. We present three examples – one involving a Hain-Lüst type operator, one involving a perturbed Friedrichs operator and one involving a simple ordinary differential operators on a half line – which together indicate that the abstract results are probably best possible.
| 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 11:00 |
| Last Modified: | 21 Dec 2011 11:17 |
| Resource URI: | http://kar.kent.ac.uk/id/eprint/23933 (The current URI for this page, for reference purposes) |
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