Toeplitz operators and Wiener-Hopf factorisation: an introduction

Toeplitz operators and Wiener-Hopf factorisation: an introduction

Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces Hp of the upper half-plane and we review how their Fredholm properties can be studied in terms of a Wiener-Hopf factorisation of their symbols, obtaining nec...

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Bibliographic Details
Main Author: Câmara M. Cristina
Format: Article
Language:English
Published: De Gruyter 2017-11-01
Series:Concrete Operators
Subjects:
toeplitz operator
wiener-hopf factorisation
singular integral equations
45e10
47a68
47b35
Online Access:https://doi.org/10.1515/conop-2017-0010
id doaj-16575a5ace7f4d1198b1f5bd4eaaf035
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spelling doaj-16575a5ace7f4d1198b1f5bd4eaaf0352021-09-06T19:19:43ZengDe GruyterConcrete Operators2299-32822017-11-014113014510.1515/conop-2017-0010conop-2017-0010Toeplitz operators and Wiener-Hopf factorisation: an introductionCâmara M. Cristina0Center for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, PortugalWiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces Hp of the upper half-plane and we review how their Fredholm properties can be studied in terms of a Wiener-Hopf factorisation of their symbols, obtaining necessary and sufficient conditions for the operator to be Fredholm or invertible, as well as formulae for their inverses or one-sided inverses when these exist. The results are applied to a class of singular integral equations in L−1(ℝ)https://doi.org/10.1515/conop-2017-0010toeplitz operatorwiener-hopf factorisationsingular integral equations45e1047a6847b35
collection DOAJ
language English
format Article
sources DOAJ
author Câmara M. Cristina
spellingShingle Câmara M. Cristina
Toeplitz operators and Wiener-Hopf factorisation: an introduction
Concrete Operators
toeplitz operator
wiener-hopf factorisation
singular integral equations
45e10
47a68
47b35
author_facet Câmara M. Cristina
author_sort Câmara M. Cristina
title Toeplitz operators and Wiener-Hopf factorisation: an introduction
title_short Toeplitz operators and Wiener-Hopf factorisation: an introduction
title_full Toeplitz operators and Wiener-Hopf factorisation: an introduction
title_fullStr Toeplitz operators and Wiener-Hopf factorisation: an introduction
title_full_unstemmed Toeplitz operators and Wiener-Hopf factorisation: an introduction
title_sort toeplitz operators and wiener-hopf factorisation: an introduction
publisher De Gruyter
series Concrete Operators
issn 2299-3282
publishDate 2017-11-01
description Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces Hp of the upper half-plane and we review how their Fredholm properties can be studied in terms of a Wiener-Hopf factorisation of their symbols, obtaining necessary and sufficient conditions for the operator to be Fredholm or invertible, as well as formulae for their inverses or one-sided inverses when these exist. The results are applied to a class of singular integral equations in L−1(ℝ)
topic toeplitz operator
wiener-hopf factorisation
singular integral equations
45e10
47a68
47b35
url https://doi.org/10.1515/conop-2017-0010
work_keys_str_mv AT camaramcristina toeplitzoperatorsandwienerhopffactorisationanintroduction
_version_ 1717777915306835968

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