On the over determinedness of some functional equations
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.
Received: December 2002; Revised: May 2003; Available Online: October 2003.
2014 IF (1 year).972