Distributional methods for functional equations

Summary.

At the 37^th International Symposium on Functional Equations (Huntington, West Virginia, May 16—23, 1999) the author presented a distributional method for solving certain functional equations of the form¶¶$\sum^N_{k=0}c_k(\xi)f_k(F_k(\xi))=0,\quad \xi\in\Omega$.¶Here $\Omega$ is a region (nonempty, open, connected set) in ${\Bbb R}^{n},\,c_k : \Omega \rightarrow {\Bbb C}$ are given $C^\infty$ functions and $F_k : \Omega \rightarrow {\Bbb R}^{m_k}$ are given submersions for $0\leq k\leq N$>. In this paper we further exploit that method to determine the continuous, locally integrable and distributional solutions of two such equations introduced at the same meeting, one by Z. Daróczy and the other by K. Heuvers.