Some classes of Wiener--Hopf plus Hankel operators and the Coburn-Simonenko Theorem

Abstract

Wiener-Hopf plus Hankel operators $W(a)+H(b):L^p({\mathbb{R}}^{+})\to L^p({\mathbb{R}}^{+})$ with generating functions $a$ and $b$ from a subalgebra of $L^{\infty }(\mathbb{R})$ containing almost periodic functions and Fourier images of $L^1(\mathbb{R})$-functions are studied. For $a$ and $b$ satisfying the so-called matching condition \begin{equation*} a(t) a(-t)=b(t) b(-t), \quad t\in \mathbb{R}, \end{equation*} we single out some classes of operators $W(a)+H(b)$ which are subject to Coburn-Simonenko theorem.

arXiv comment20 pages