On Restricting Cauchy-Pexider Equations to Submanifolds
Classical Analysis and ODEs
2013-01-11 v2
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.
Cite
@article{arxiv.1203.5370,
title = {On Restricting Cauchy-Pexider Equations to Submanifolds},
author = {Marcos Charalambides},
journal= {arXiv preprint arXiv:1203.5370},
year = {2013}
}
Comments
20 pages; to appear in Aequationes Mathematicae; modified title slightly, updated references