On Wiener-Hopf operators over linearly ordered diskrete Abelian groups

Abstract

Let $X$ denotes a discrete linearly ordered Abelian group, and let $X_{+}$ be the positive cone in $X$. In this note we compute the Fredholm index and study spectral properties of Wiener-Hopf operators $W_{k}g=1_{X_{+}}(k\ast g)$, $k\in l_2(X_{+})$ in the space $l_2(X_{+})$ in terms of their symbols $\check{k}$ where $\check{k}$ stands for the inverse Fourier transform of $k$.