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Invertibility issues for a class of Wiener–Hopf plus Hankel operators
Journal of Spectral Theory ( IF 1.0 ) Pub Date : 2021-07-14 , DOI: 10.4171/jst/359
Victor D. Didenko 1 , Bernd Silbermann 2
Affiliation  

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.

中文翻译:

一类 Wiener-Hopf 加 Hankel 算子的可逆性问题

研究了Wiener–Hopf 加Hankel 算子$W(a)+H(b)$ 作用于空间$L^p(\mathbb{R}^+)$, $1 \leq p<\infty$ 的可逆性。如果 $a$ 和 $b$ 属于 $L^\infty(\mathbb{R})$ 的子代数并且满足条件 $$ a(t) a(-t)=b(t) b(-t ),\quad t\in\mathbb{R}, $$ 我们建立了算子 $W(a)+H(b)$ 为单边可逆、可逆或广义可逆的充分必要条件。此外,还给出了相应逆的有效表示。
更新日期:2021-07-21
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