Communications in Mathematical Sciences

Volume 22 (2024)

Number 5

Representation theorem for multivariable totally symmetric functions

Pages: 1195 – 1201

DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n5.a2

Authors

Chongyao Chen (Department of Mathematics, Duke University, Durham, NC, USA)

Ziang Chen (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA)

Jianfeng Lu (Departments of Mathematics, Physics, and Chemistry, Duke University, Durham, NC, USA)

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.

Keywords

multisymmetric functions, representation, singularity

2010 Mathematics Subject Classification

26B05, 26B40, 26C99, 54C30

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The work of Z. Chen and J. Lu is supported in part by the National Science Foundation via awards DMS-2012286 and DMS-2309378.

Received 10 June 2023

Received revised 18 October 2023

Accepted 3 November 2023

Published 15 July 2024