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The Detectable Subspace for the Friedrichs Model

Brown, B.M., Marletta, Marco, Naboko, Sergey, Wood, Ian (2019) The Detectable Subspace for the Friedrichs Model. Integral Equations and Operator Theory, . ISSN 0378-620X. E-ISSN 1420-8989. (doi:10.1007/s00020-019-2548-9)

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Abstract

This paper discusses how much information on a Friedrichs model operator can be detected from `measurements on the boundary'. We use the framework of boundary triples to introduce the generalised Titchmarsh-Weyl M-function and the detectable subspaces which are associated with the part of the operator which is `accessible from boundary measurements'. The Friedrichs model, a finite rank perturbation of the operator of multiplication by the independent variable, is a toy model that is used frequently in the study of perturbation problems. We view the Friedrichs model as a key example for the development of the theory of detectable subspaces, because it is sufciently simple to allow a precise description of the structure of the detectable subspace in many cases, while still exhibiting a variety of behaviours. The results also demonstrate an interesting interplay between modern complex analysis, such as the theory of Hankel operators, and operator theory

Item Type: Article
DOI/Identification number: 10.1007/s00020-019-2548-9
Uncontrolled keywords: Friedrichs model; operator theory; complex analysis
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Ian Wood
Date Deposited: 27 Sep 2019 15:54 UTC
Last Modified: 22 Nov 2019 12:14 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/76860 (The current URI for this page, for reference purposes)
Wood, Ian: https://orcid.org/0000-0001-7181-7075
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