Some Results on the Invertibility of Wiener-Hopf-Hankel Operators

Abstract

A study is presented on the invertibility properties of scalar operators defined as the sum of a Wiener-Hopf and a Hankel operator on $L_2({\mathbb{R}}^{+})$ with symbols in $L_{\infty }(\mathbb{R})$. This study is based on the properties of a vector Wiener-Hopf operator naturally associated with each of the operators mentioned above. The results obtained are applied to problems in Diffraction Theory.