Spherical Functions on Fuzzy Lie group

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