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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| Format: | Article |
| Language: | English |
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De Gruyter
2017-11-01
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| Series: | Concrete Operators |
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| Online Access: | https://doi.org/10.1515/conop-2017-0010 |
| Summary: | 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) |
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| ISSN: | 2299-3282 |