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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 $\mathbb R^n$.
Mathematics Subject Classification: 37N99, 35L35.

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