Solving Chisini's functional equation
Functional Analysis
2010-07-01 v2
Abstract
We investigate the n-variable real functions G that are solutions of the Chisini functional equation F(x)=F(G(x),...,G(x)), where F is a given function of n real variables. We provide necessary and sufficient conditions on F for the existence and uniqueness of solutions. When F is nondecreasing in each variable, we show in a constructive way that if a solution exists then a nondecreasing and idempotent solution always exists. We also provide necessary and sufficient conditions on F for the existence of continuous solutions and we show how to construct such a solution. We finally discuss a few applications of these results.
Keywords
Cite
@article{arxiv.0903.1546,
title = {Solving Chisini's functional equation},
author = {Jean-Luc Marichal},
journal= {arXiv preprint arXiv:0903.1546},
year = {2010}
}