S. S. Sangodele | Searcharxiv

arXiv2026

Haar Measure on Fuzzy Lie Group

Let $\mathfrak{G}$ be a locally compact Lie group and $dμ$ a Haar measure defined on $\mathfrak{G}$. We consider the existence of a fuzzy analogue of $\mathfrak{G}$ denoted by $\mathfrak{G_f}$ called a fuzzy Lie group and develop a fuzzy Haar measure $μ_f$ on $\mathfrak{G_f}$. Also we construct a fuzzy Haar integral with respect to the corresponding fuzzy Haar measure on $\mathfrak{G_f}$. And finally we show that there exists a fuzzy Haar integral that is unique up to a multiplicative constant.

math.GM↗

arXiv2022

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 $\mathfrak{G_f}$ 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 $\mathfrak{G_f}.$

math.GM↗