Representation Theorem for Multivariable Totally Symmetric Functions
Classical Analysis and ODEs
2024-12-25 v4
Abstract
In this work, we establish a representation theorem for multivariable totally symmetric functions: a multisymmetric continuous function must be the composition of a continuous function and a set of generators of the multisymmetric polynomials. We then study the singularity and geometry of the generators, and show that the regularity may become worse after applying the decomposition.
Cite
@article{arxiv.2211.15958,
title = {Representation Theorem for Multivariable Totally Symmetric Functions},
author = {Chongyao Chen and Ziang Chen and Jianfeng Lu},
journal= {arXiv preprint arXiv:2211.15958},
year = {2024}
}