Linear independence of iterates and entire solutions of functional equations

Christensen, Jens Peter Reus; Fischer, Pal

doi:10.1090/S0002-9939-1988-0954993-9

Linear independence of iterates and entire solutions of functional equations
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by Jens Peter Reus Christensen and Pal Fischer PDF

Proc. Amer. Math. Soc. 103 (1988), 1120-1124 Request permission

Abstract:

A classical result of Pólya concerning the growth of Nevanlinna’s characteristics of composite functions is used to prove linear independence of some iterates. The same result of Pólya is also used to show the nonexistence of entire solutions of the Feigenbaum functional equation.

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