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

Brown, Malcolm S. 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 available from this repository)

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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: 25 Nov 2014 11:20
Resource URI: http://kar.kent.ac.uk/id/eprint/23933 (The current URI for this page, for reference purposes)
ORCiD (Brown, Malcolm S.):
ORCiD (Hinchcliffe, James):
ORCiD (Marletta, Marco):
ORCiD (Naboko, Serguei):
ORCiD (Wood, Ian):
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