On an Application of Hypoellipticity to Solutions of Functional Equations
funct-an
2016-08-31 v1 Functional Analysis
Abstract
We study the regularity of solutions of functional equations of a generalized mean value type. In this paper we give sufficient conditions for the regularity by using hypoellipticity which is a concept of the theory of partial differential equations. Further we also give an affirmative answer to a conjecture of H.\'Swiatak. A part of the results was announced in the comprehensive paper [8] on series of our joint works. To prove the regularity of solutions of functional equation is in general one of central problem in the theory of functional equations.
Cite
@article{arxiv.funct-an/9409002,
title = {On an Application of Hypoellipticity to Solutions of Functional Equations},
author = {A. Tsutsumi and S. Haruki},
journal= {arXiv preprint arXiv:funct-an/9409002},
year = {2016}
}
Comments
9 pages, LaTeX