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arXiv · 1710.11572

Toeplitz operators and Wiener-Hopf factorisation: an introduction

M. Cristina Câmara
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Abstract

Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces $H^p$ 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 $L^p(\mathbb R)$.

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M. Cristina Câmara. 2017-10-31. Toeplitz operators and Wiener-Hopf factorisation: an introduction. https://arxiv.org/abs/1710.11572

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