The abstract Titchmarsh-Weyl M-function for adjoint operator pairs and its relation to the spectrum

Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Hinchcliffe, James, Marletta, Marco, 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. 10.1007/s00020-009-1668-z

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Abstract

n 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)\tilde] 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
Date Type:	Publication
Status:	Published
Schools:	Schools > Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Uncontrolled Keywords:	M-function - boundary triples - adjoint pairs - spectrum
Publisher:	Springer
ISSN:	0378-620X
Last Modified:	18 Oct 2022 13:21
URI:	https://orca.cardiff.ac.uk/id/eprint/13561

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