Annales AcademiŠ Scientiarum FennicŠ
Mathematica
Volumen 32, 2007, 151-170

ON A CLASS OF COMPLEX FUNCTIONAL EQUATIONS

Jarkko Rieppo

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 Schr÷der 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, Schr÷der 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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