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)
@article{bwmeta1.element.doi-10_1515_conop-2017-0010,
author = {M. Cristina C\^amara},
title = {Toeplitz operators and Wiener-Hopf factorisation: an introduction},
journal = {Concrete Operators},
volume = {4},
year = {2017},
pages = {130-145},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_conop-2017-0010}
}
M. Cristina Câmara. Toeplitz operators and Wiener-Hopf factorisation: an introduction. Concrete Operators, Tome 4 (2017) pp. 130-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_conop-2017-0010/