Differences of functions and measures

Abstract

Throughout this paper, G will denote a locally compact Hausdorff group with a chosen left Haar measure m. For each s ∈ G, τs denotes the left translation operator which acts on functions ƒ according to the rule; τsƒ(x) = ƒ(s−1x) and on measures or distributions in the corresponding way. The associted left difference operators ts−1 is denoted by Δs. On occasions it will be more convenient to write τ(s) and Δ(s) in place of τs and Δs.