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Abstract Banach Convolution Function Modules over Coset Spaces of Compact Subgroups in Locally compact Groups

  • Arash Ghaani FarashahiEmail author
Article
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Abstract

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 \(\mu \) be the normalized G-invariant measure over the homogeneous space G / H associated to the Weil’s formula and \(1\le p<\infty \). We then introduce the notion of convolution left-module action of \(L^1(G/H,\mu )\) on the Banach function spaces \(L^p(G/H,\mu )\).

Keywords

Homogeneous space Locally compact group Compact subgroup Convolution Involution Module action 

Mathematics Subject Classification

Primary 43A85 Secondary 43A10 43A15 43A20 

Notes

References

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Copyright information

© Sociedade Brasileira de Matemática 2019

Authors and Affiliations

  1. 1.Laboratory for Computational Sensing and Robotics (LCSR), Whiting School of EngineeringJohns Hopkins UniversityBaltimoreUSA

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