Abstract
Let G be a locally compact, compactly generated group of polynomial growth and let ω be a weight on G. Under proper assumptions on the weight ω, the Banach space Lp(G,ω) is a Banach ∗-algebra. In this paper we give examples of such weighted Lp-algebras and we study some of their harmonic analysis properties, such as symmetry, existence of functional calculus, regularity, weak Wiener property, Wiener property, and existence of minimal ideals of a given hull.
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