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Author: Jean-Luc Marichal . . . . Institute: University of Luxembourg, Luxembourg . . . . . Co-author(s): . . . . Title of talk: Solving Chisini’s functional equation . . . .

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48

th

International Symposium on Functional Equations

Batz-sur-Mer, France, June 13–18, 2010

Abstract Form

Author: Jean-Luc Marichal . . . . Institute: University of Luxembourg, Luxembourg . . . . . Co-author(s): . . . . Title of talk: Solving Chisini’s functional equation . . . .

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.

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