The detectable subspace for the Friedrichs model
| Autor: | Brian Malcolm Brown, Marco Marletta, Sergey Naboko, Ian Wood |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
media_common.quotation_subject Perturbation (astronomy) 01 natural sciences Mathematics - Spectral Theory Operator (computer programming) 0103 physical sciences Classical Analysis and ODEs (math.CA) FOS: Mathematics 0101 mathematics QA Bitwise operation Spectral Theory (math.SP) Mathematics media_common Algebra and Number Theory Toy model Variables 010102 general mathematics Linear subspace Functional Analysis (math.FA) Mathematics - Functional Analysis Mathematics - Classical Analysis and ODEs 010307 mathematical physics Analysis Subspace topology |
| ISSN: | 0378-620X |
| Popis: | 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. Comment: arXiv admin note: substantial text overlap with arXiv:1404.6820 |
| Databáze: | OpenAIRE |
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