Wiener–Hopf Operators on Spaces of Functions on $${\mathbb{R}}^{+}$$ with Values in a Hilbert Space

Abstract

A Wiener–Hopf operator on a Banach space of functions on \({\mathbb{R}}^{+}\) is a bounded operator T such that P+S−aTSa = T, a ≥ 0, where Sa is the operator of translation by a. We obtain a representation theorem for the Wiener–Hopf operators on a large class of functions on \({\mathbb{R}}^{+}\) with values in a separable Hilbert space.