February  2004, 10(1&2): 497-505. doi: 10.3934/dcds.2004.10.497

On the over determinedness of some functional equations

1. 

Department of Mathematics, Technion, Haifa, 32000, Israel

Received  December 2002 Revised  May 2003 Published  October 2003

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 $\mathbb R^n$.
Citation: Boris Paneah. On the over determinedness of some functional equations. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 497-505. doi: 10.3934/dcds.2004.10.497
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