The detectable subspace for the Friedrichs model
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Publication:6324443
DOI10.1007/S00020-019-2548-9arXiv1908.11717WikidataQ115180794 ScholiaQ115180794MaRDI QIDQ6324443
B. M. Brown, Serguei Naboko, Marco Marletta, I. G. Wood
Publication date: 29 August 2019
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 -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.
Spectrum, resolvent (47A10) General spectral theory of ordinary differential operators (34L05) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Integral operators (47G10) Hardy spaces (30H10)
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