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

Brown, Brian Malcolm, Hinchcliffe, James, Marletta, Marco, Naboko, Serguei, 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. (doi:10.1007/s00020-009-1668-z) (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) (KAR id:23933)

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.
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
DOI/Identification number:	10.1007/s00020-009-1668-z
Subjects:	Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Institutional Unit:	Schools > School of Engineering, Mathematics and Physics > Mathematical Sciences
Former Institutional Unit:	Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User:	Ian Wood
Date Deposited:	09 Apr 2010 11:00 UTC
Last Modified:	20 May 2025 11:34 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/23933 (The current URI for this page, for reference purposes)

University of Kent Author Information

Naboko, Serguei.

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CReDIT Contributor Roles:

Wood, Ian.

Creator's ORCID:	https://orcid.org/0000-0001-7181-7075
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