Power boundedness in Fourier and Fourier-Stieltjes algebra of an ultraspherical hypergroup

TL;DR

This paper investigates the properties of power boundedness and Cesàro boundedness within the Fourier and Fourier-Stieltjes algebras of ultraspherical hypergroups, providing characterizations for these properties.

Contribution

It offers new characterizations of power boundedness in the Fourier and Fourier-Stieltjes algebras associated with ultraspherical hypergroups.

Findings

Characterization of power boundedness in $A(H)$ and $B(H)$

Analysis of Cesàro boundedness in $B(H)$

Extension of boundedness concepts to ultraspherical hypergroups

Abstract

Let $H$ be an ultraspherical hypergroup associated with a locally compact group $G$ and a spherical projector $\pi$ and let $A(H)$ and $B(H)$ denote the Fourier and Fourier-Stieltjes algebras, respectively, associated with $H.$ In this note, we study power boundedness and Ces\`aro boundedness in $B(H)$. We also characterize the power bounded property for both $A(H)$ and $B(H).$