On Fourier algebra of a hypergroup constructed from a conditional expectation on a locally compact group

TL;DR

This paper demonstrates that the Fourier space of a hypergroup derived from a conditional expectation on a locally compact group forms a Banach algebra, extending the understanding of harmonic analysis on hypergroups.

Contribution

It establishes the Banach algebra structure of the Fourier space for hypergroups constructed via conditional expectations on locally compact groups, a novel theoretical result.

Findings

Fourier space of the hypergroup is a Banach algebra

Extension of harmonic analysis to hypergroups from groups

New structural insights into hypergroup Fourier analysis

Abstract

We prove that the Fourier space of a hypergroup constructed from a conditional expectation on a locally compact group has a Banach algebra structure.