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On the over determinedness of some functional equations
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 $\mathbb R^n$.