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The detectable subspace for the Friedrichs model - applications of Toeplitz operators and the Riesz-Nevanlinna factorisation theorem

Naboko, S., Wood, I. (2020) The detectable subspace for the Friedrichs model - applications of Toeplitz operators and the Riesz-Nevanlinna factorisation theorem. Annales Henri Poincaré, . ISSN 1424-0637. (In press) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided) (KAR id:81954)

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Abstract

We discuss how much information on a Friedrichs model operator (a finite rank perturbation of the operator of multiplication by the independent variable) can be detected from ‘measurements on the boundary’. The framework of boundary triples is used 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’. In this paper we choose functions arising as parameters in the Friedrichs model in certain Hardy classes. This allows us to determine the detectable subspace by using the canonical Riesz-Nevanlinna factorisation of the symbol of a related Toeplitz operator.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Ian Wood
Date Deposited: 02 Jul 2020 09:15 UTC
Last Modified: 02 Jul 2020 09:15 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/81954 (The current URI for this page, for reference purposes)
Wood, I.: https://orcid.org/0000-0001-7181-7075
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