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arXiv · 1103.3610

Harmonic analysis of weighted $L^p$-algebras

Yulia N. Kuznetsova·C. Molitor-Braun
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Abstract

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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BibTeXRIS

Yulia N. Kuznetsova, C. Molitor-Braun. 2011-03-18. Harmonic analysis of weighted $L^p$-algebras. https://doi.org/10.1016/j.exmath.2012.01.002

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