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The detectable subspace for the Friedrichs model

Brown, Brian M., Marletta, Marco, Naboko, Sergey and Wood, Ian 2019. The detectable subspace for the Friedrichs model. Integral Equations and Operator Theory 91 , 49. 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 sufficiently 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
Date Type: Publication
Status: Published
Schools: Mathematics
Computer Science & Informatics
Additional Information: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Publisher: Springer Verlag (Germany)
ISSN: 0378-620X
Funders: Russian Foundation for Basic Research, Knut and Alice Wallenberg Foundation
Date of First Compliant Deposit: 30 September 2019
Date of Acceptance: 27 September 2019
Last Modified: 13 Nov 2019 14:47
URI: http://orca-mwe.cf.ac.uk/id/eprint/125702

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