Invertibility Issues for Toeplitz plus Hankel Operators and Their Close Relatives

2020/03/20 by Didenko, Victor, Silbermann, Bernd
#45E10 #47B38 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47B35 #Secondary 47B33

paper · doi:10.48550/arxiv.2003.09115

Abstract

The paper describes various approaches to the invertibility of Toeplitz plus Hankel operators in Hardy and l^p-spaces, integral and difference Wiener-Hopf plus Hankel operators and generalized Toeplitz plus Hankel operators. Special attention is paid to a newly developed method, which allows to establish necessary, sufficient and also necessary and sufficient conditions of invertibility, one-sided and generalized invertibility for wide classes of operators and derive efficient formulas for the corresponding inverses. The work also contains a number of problems whose solution would be of interest in both theoretical and applied contexts.

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