Functional Calculus in Weighted Group Algebras

Abstract

Let G be a compactly generated, locally compact group with polynomial growth and let ! be a weight on G. We look for general conditions on the weight which allow us to develop a functional calculus on a total part of L1(G, !). This functional calculus is then used to study harmonic analysis properties of L1(G, !), such as the Wiener property and Domar’s theorem.