Standard

The Detectable Subspace for the Friedrichs Model. / Brown, B. M.; Marletta, M.; Naboko, S.; Wood, I. G.

In: Integral Equations and Operator Theory, Vol. 91, No. 5, 49, 01.10.2019.

Research output: Contribution to journal › Article › peer-review

Harvard

Brown, BM, Marletta, M, Naboko, S & Wood, IG 2019, 'The Detectable Subspace for the Friedrichs Model', Integral Equations and Operator Theory, vol. 91, no. 5, 49. https://doi.org/10.1007/s00020-019-2548-9

APA

Brown, B. M., Marletta, M., Naboko, S., & Wood, I. G. (2019). The Detectable Subspace for the Friedrichs Model. Integral Equations and Operator Theory, 91(5), [49]. https://doi.org/10.1007/s00020-019-2548-9

Vancouver

Brown BM, Marletta M, Naboko S, Wood IG. The Detectable Subspace for the Friedrichs Model. Integral Equations and Operator Theory. 2019 Oct 1;91(5). 49. https://doi.org/10.1007/s00020-019-2548-9

Author

Brown, B. M. ; Marletta, M. ; Naboko, S. ; Wood, I. G. / The Detectable Subspace for the Friedrichs Model. In: Integral Equations and Operator Theory. 2019 ; Vol. 91, No. 5.

BibTeX

@article{58301876c15147ad8ae0b2da61e1c650,
title = "The Detectable Subspace for the Friedrichs Model",
abstract = "This paper discusses how much information on a Friedrichs model operator can be detected from {\textquoteleft}measurements on the boundary{\textquoteright}. 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 {\textquoteleft}accessible from boundary measurements{\textquoteright}. 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.",
keywords = "Detectable subspace, Friedrichs model, Inverse problem, M-function, GENERALIZED RESOLVENTS, OPERATOR, INVERSE PROBLEMS",
author = "Brown, {B. M.} and M. Marletta and S. Naboko and Wood, {I. G.}",
year = "2019",
month = oct,
day = "1",
doi = "10.1007/s00020-019-2548-9",
language = "English",
volume = "91",
journal = "Integral Equations and Operator Theory",
issn = "0378-620X",
publisher = "Birkh{\"a}user Verlag AG",
number = "5",

}

RIS

TY - JOUR

T1 - The Detectable Subspace for the Friedrichs Model

AU - Brown, B. M.

AU - Marletta, M.

AU - Naboko, S.

AU - Wood, I. G.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

KW - Detectable subspace

KW - Friedrichs model

KW - Inverse problem

KW - M-function

KW - GENERALIZED RESOLVENTS

KW - OPERATOR

KW - INVERSE PROBLEMS

UR - http://www.scopus.com/inward/record.url?scp=85073510738&partnerID=8YFLogxK

U2 - 10.1007/s00020-019-2548-9

DO - 10.1007/s00020-019-2548-9

M3 - Article

AN - SCOPUS:85073510738

VL - 91

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 5

M1 - 49

ER -

ID: 49775481