Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 32, 2007, 151-170
University of Joensuu, Department of Physics and Mathematics
P.O. Box 111, FI-80101 Joensuu, Finland; jarkko.rieppo 'at' jns.fi
Abstract. We consider a class of complex functional equations that admit transcendental meromorphic solutions with relatively few distinct poles. The solutions are characterized and it is shown that they must also satisfy a functional equation of the certain simple form. The equations that are considered contains e.g. some delay equations and the generalized Schröder equation as special cases. The reasoning relies on the combination of Nevanlinna theory and algebraic field theory.
2000 Mathematics Subject Classification: Primary 30D05; Secondary 30D35, 39B32.
Key words: Complex functional equation, Schröder equation, hypertranscendency, Nevanlinna theory, value distribution theory.
Reference to this article: J. Rieppo: On a class of complex functional equations. Ann. Acad. Sci. Fenn. Math. 32 (2007), 151-170.
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