On Restricting Cauchy-Pexider Equations to Submanifolds

Abstract

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.

20 pages; to appear in Aequationes Mathematicae; modified title slightly, updated references

References in corpus (1)

• Near-extremizers of Young's Inequality for R^d

Cited by in corpus (5)

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• On extremisers to a bilinear Strichartz inequality