Solving Chisini's functional equation

Details Solving Chisini's functional equation Solving Chisini's functional equation

2009-03-09

arxiv.org/abs/0903.1546v2

Aequationes Mathematicae 79 (3) (2010) 237-260

Mathematics

Functional Analysis

Scientific paper

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.

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