On Restricting Cauchy-Pexider Equations to Submanifolds
arXiv:1203.5370 · doi:10.1007/s00010-012-0173-7
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