A novel approach through spherical functions in the characterization of invariant functions

Orbita Mathematicae 2026 Open access

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Authors: Rocío Díaz Marín, Linda V. Saal
DOI: 10.2140/om.2027.4.67
Cited by: 0
References: 18

Abstract

Given a compact subgroup K of the orthogonal group acting on the Euclidean space ‫ޒ‬ n , Gerald Schwarz proved that every smooth K -invariant function on ‫ޒ‬ n can be expressed as a smooth function of a generating set of K -invariant polynomials on n variables.Our goal is to provide an alternative and more straightforward proof of this result, based on Gelfand theory, with a particular focus on spherical functions.

Fields of Study & Subjects

Mathematical functions and polynomials Advanced Optimization Algorithms Research Advanced Mathematical Theories and Applications

Publication details

Journal / source
Orbita Mathematicae
Volume
4
Issue
1
Pages
67–84
Publication date
1 August 2026
Language
EN