The Abstract TITCHMARSH-WEYL M-Function for adjoint operator pairs and its relation to the Spectrum

Brown, Brian Malcolm and Hinchcliffe, James and Marletta, Marco and Naboko, Serguei and Wood, Ian (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 currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not available from this repository. (Contact us about this Publication)
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: 10 Dec 2014 18:15
Resource URI: https://kar.kent.ac.uk/id/eprint/23933 (The current URI for this page, for reference purposes)
  • Depositors only (login required):