Invertibility issues for a class of Wiener–Hopf plus Hankel operators

The invertibility of Wiener–Hopf plus Hankel operators W(a)+H(b) acting on the spaces L^p(\mathbb{R}^+) , 1 \leq p<\infty is studied. If a and b belong to a subalgebra of L^\infty(\mathbb{R}) and satisfy the condition a(t) a(-t)=b(t) b(-t),\quad t\in\mathbb{R}, we establish necessary and also suf...

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Bibliographic Details
Published inJournal of spectral theory Vol. 11; no. 2; pp. 847 - 872
Main Authors Didenko, Victor D., Silbermann, Bernd
Format Journal Article
LanguageEnglish
Published European Mathematical Society Publishing House 01.01.2021
Subjects
Functions, Inverse
Mathematical research
Operator theory
China
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ISSN1664-039X
1664-0403
DOI10.4171/jst/359

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Summary:The invertibility of Wiener–Hopf plus Hankel operators W(a)+H(b) acting on the spaces L^p(\mathbb{R}^+) , 1 \leq p<\infty is studied. If a and b belong to a subalgebra of L^\infty(\mathbb{R}) and satisfy the condition a(t) a(-t)=b(t) b(-t),\quad t\in\mathbb{R}, we establish necessary and also sufficient conditions for the operators W(a)+H(b) to be one-sided invertible, invertible or generalized invertible. Besides, efficient representations for the corresponding inverses are given.
ISSN:1664-039X
1664-0403
DOI:10.4171/jst/359