Toeplitz operators and Wiener-Hopf factorisation: an introduction. (English) Zbl 1392.45007
Summary: Wiener-Hopf factorization 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 \(L^p(\mathbb{R})\).
MSC:
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 47A68 | Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators |
| 47B35 | Toeplitz operators, Hankel operators, Wiener-Hopf operators |
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