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E Hewitt, KA Ross (1979)
10.1007/978-1-4419-8638-2Abstract Harmonic Analysis: Volume I Structure of Topological Groups Integration Theory Group Representations. Grundlehren der mathematischen Wissenschaften, vol. 115
This paper presents an operator theory approach for the abstract structure of Banach function modules over coset spaces of compact subgroups. Let G be a locally compact group and H be a compact subgroup of G. Let μ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mu $$\end{document} be the normalized G-invariant measure over the homogeneous space G / H associated to the Weil’s formula and 1≤p<∞\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$1\le p<\infty $$\end{document}. We then introduce the notion of convolution left-module action of L1(G/H,μ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^1(G/H,\mu )$$\end{document} on the Banach function spaces Lp(G/H,μ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^p(G/H,\mu )$$\end{document}.
"Bulletin of the Brazilian Mathematical Society, New Series" – Springer Journals
Published: Jun 1, 2022
Keywords: Homogeneous space; Locally compact group; Compact subgroup; Convolution; Involution; Module action; Primary 43A85; Secondary 43A10; 43A15; 43A20
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