Functional equations and harmonic extensions
- 1 January 1994
- journal article
- research article
- Published by Taylor & Francis in Complex Variables and Elliptic Equations
- Vol. 24 (1-2) , 121-129
- https://doi.org/10.1080/17476939408814705
Abstract
In this paper, we first consider the posibility of extending to the exterior of a region the solution to a Dirichlet problem. We limit ourselves to the situation where the boundary curve is analytic and the boundary data is polynomial or real-entire. We then turn to the problem of hte existence of solutions to the functional equation f(P(z))-g(Q(z)) = k(z),, where P and Q are given polynomials and k is a given meromorphic function. Central to our results is a generalization of a theorem of A. and C. Rényiconcerning periodic functions of the form f(P). We conclude by showing how the two problems ae related.Keywords
This publication has 4 references indexed in Scilit:
- Dirichlet's Problem When the Data is an Entire FunctionBulletin of the London Mathematical Society, 1992
- An Algebraic Theorem of E. Fischer, and the Holomorphic Goursat ProblemBulletin of the London Mathematical Society, 1989
- A Theorem on Level Curves of Harmonic FunctionsJournal of the London Mathematical Society, 1969
- Some remarks on periodic entire functionsJournal d'Analyse Mathématique, 1965