On an Application of Hypoellipticity to Solutions of Functional Equations

Details On an Application of Hypoellipticity to Solutions of Functional Equations On an Application of Hypoellipticity to Solutions of Functional Equations

1994-09-21

arxiv.org/abs/funct-an/9409002v1

Mathematics

Functional Analysis

9 pages, LaTeX

Scientific paper

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.

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