On the over determinedness of some functional equations

Boris Paneah

doi:10.3934/dcds.2004.10.497

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2004, Volume 10, Issue 1&2: 497-505. Doi: 10.3934/dcds.2004.10.497

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On the over determinedness of some functional equations

Boris Paneah^1,

1.
Department of Mathematics, Technion, Haifa, 32000

Received: November 30, 2002

Revised: April 30, 2003

Published: December 2003

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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 $\mathbb R^n$.

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Mathematics Subject Classification: 37N99, 35L35.

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