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

Abstract

The invertibility of Wiener–Hopf plus Hankel operators $W(a)+H(b)$ acting on the spaces $L^p({\mathbb{R}}^{+})$, $1\le p<\infty$ is studied. If $a$ and $b$ belong to a subalgebra of $L^{\infty }(\mathbb{R})$ and satisfy the condition

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.