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Concrete Operators

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Mathematical Citation Quotient (MCQ) 2017: 0.34

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Toeplitz operators and Wiener-Hopf factorisation: an introduction

M. Cristina Câmara
  • Center for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal
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Published Online: 2017-11-09 | DOI: https://doi.org/10.1515/conop-2017-0010


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)

Keywords: Toeplitz operator; Wiener-Hopf factorisation; Singular integral equations

MSC 2010: 45E10; 47A68; 47B35


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About the article

Received: 2017-03-22

Accepted: 2017-09-06

Published Online: 2017-11-09

Published in Print: 2017-11-27

Citation Information: Concrete Operators, Volume 4, Issue 1, Pages 130–145, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2017-0010.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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