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.
|The full text of this publication is not available from this repository. (Contact us about this Publication)|
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.
|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)|
- Depositors only (login required):