A novel approach through spherical functions in the characterization of invariant functions
Functional Analysis
2025-10-14 v3 Group Theory
Spectral Theory
Abstract
Given a compact subgroup K of the orthogonal group acting on the Euclidean space Rn, Gerald Schwarz proved that every smooth K-invariant function on Rn can be expressed as a smooth function of a generating set of -invariant polynomials on n variables. The goal of this work is to provide an alternative and more straightforward proof of this result, based on Gelfand theory, with a particular focus on spherical functions.
Keywords
Cite
@article{arxiv.2510.01043,
title = {A novel approach through spherical functions in the characterization of invariant functions},
author = {Rocío Díaz Martín and Linda Saal},
journal= {arXiv preprint arXiv:2510.01043},
year = {2025}
}