Spherical Functions on Fuzzy Lie group

TL;DR

This paper introduces fuzzy Lie groups as a generalization of classical Lie groups and constructs spherical functions on them, extending classical harmonic analysis results to this fuzzy setting.

Contribution

It develops the theory of spherical functions on fuzzy Lie groups, providing existence results analogous to Helgason's classical theorems.

Findings

Spherical functions are constructed on fuzzy Lie groups.

Existence of Helgason-spherical functions is established in the fuzzy context.

The work extends harmonic analysis to fuzzy Lie groups.

Abstract

Let $G$ be a locally compact Lie group and $\mathfrak{g}$ its Lie algebra. We consider a fuzzy analogue of $G,$ denoted by $\mathfrak{G_f}$ called a fuzzy Lie group. Spherical functions on $\mathfrak{G_f}$ are constructed and a version of the existence result of the Helgason-spherical function on $G$ is then established on $\mathfrak{G_f}.$