Beurling-Fourier Algebras on The Homogeneous Spaces

Authors

  • Motahhare Bagheri Seyghalan Ph. D Candidate at University of Guilan
  • marzieh Shams Yousefi University of Guilan

Keywords:

Beurling-Fourier Algebra‎, ‎homogeneous Space‎, ‎weight Inverse‎, ‎co-multiplication‎, ‎amenable group

Abstract

For a locally compact group $G$ with a closed subgroup $H$‎, ‎we define and study Beurling-Fourier algebras on the homogeneous space $G/H$‎, ‎which consists of the left cosets of $H$ in $G$‎. ‎The cornerstone of our approach is the definition of Beurling-Fourier algebras in terms of the weight inverses‎. ‎We show that our construction on $G/H$‎, ‎denoted by $A(G:H,\omega)$ and equipped with the norm ${ \Vert‎ . ‎\Vert}_{\omega} $‎, ‎forms a Banach algebra‎.

‎In particular‎, ‎we establish a version of Leptin theorem‎: ‎if $H$ is compact‎, ‎then $G$ is amenable‎, ‎if and only if Beurling-Fourier algebra on $G/H$ has a bounded approximate identity‎.

Author Biography

marzieh Shams Yousefi, University of Guilan

Assistant professor of Pure math Department

Published

2025-10-05

Issue

Vol. 19

Section

Vol. 19, No. 5, (2025)

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