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On Restricting Cauchy-Pexider Equations to Submanifolds
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math.CA
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cauchy-pexiderequationsfunctionalaffineconditionsconsidereddetermineequation
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Sufficient geometric conditions are given which determine when the Cauchy-Pexider functional equation f(x)g(y)=h(x+y) restricted to x,y lying on a hypersurface in R^d has only solutions which extend uniquely to exponential affine functions. Some related functional equations are also considered.
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