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arXiv · 2510.01043

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

Rocío Díaz Martín·Linda Saal
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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 $K$-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.

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BibTeXRIS

Rocío Díaz Martín, Linda Saal. 2025-10-01. A novel approach through spherical functions in the characterization of invariant functions. https://doi.org/10.2140/om.2027.4.67

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