Harmonic analysis of weighted $L^p$-algebras

Details Harmonic analysis of weighted $L^p$-algebras Harmonic analysis of weighted $L^p$-algebras

2011-03-18

arxiv.org/abs/1103.3610v1

Mathematics

Functional Analysis

Scientific paper

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

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