On the over determinedness of some functional equations

Pages: 497 - 505, Volume 10, Issue 1/2, January/February 2004

doi:10.3934/dcds.2004.10.497       Abstract        Full Text (142.5K)       Related Articles

Boris Paneah - Department of Mathematics, Technion, Haifa, 32000, Israel (email)

Abstract: It is shown that some well known functional equations in $\mathbb R^n, n\geq 2$, turn out to be overdetermined. This means that their solutions are uniquely defined if the corresponding relations are fulfilled not in the whole spaces $\mathbb R^n, n\geq 2$, but only at the points of some smooth submanifolds in $\mathbb R^n$.

Keywords:  Dynamical systems, functional equations, orbits, configurations, overdeterminedness.
Mathematics Subject Classification:  37N99, 35L35.

Received: December 2002;      Revised: May 2003;      Published: October 2003.