On the equation P(f)=Q(g), where P,Q are polynomials and f,g are entire functions

Details On the equation P(f)=Q(g), where P,Q are polynomials and f,g are entire functions On the equation P(f)=Q(g), where P,Q are polynomials and f,g are entire functions

2008-04-04

arxiv.org/abs/0804.0739v3

Mathematics

Complex Variables

Final version, to appear in Amer. Journal of Math

Scientific paper

In 1922 Ritt described polynomial solutions of the functional equation P(f)=Q(g). In this paper we describe solutions of the equation above in the case when P,Q are polynomials while f,g are allowed to be arbitrary entire functions. In fact, we describe solutions of the more general functional equation s=P(f)=Q(g), where s,f,g are entire functions and P,Q are arbitrary rational functions. Besides, we solve the problem of description of "strong uniqueness polynomials" for entire functions.

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