Brown, Brian M.  ORCID: https://orcid.org/0000-0002-2871-6591, Marletta, Marco ORCID: https://orcid.org/0000-0003-1546-4046, 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: | Schools > Mathematics Schools > 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: | 20 May 2023 03:47 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/125702 |
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