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On an Application of Hypoellipticity to Solutions of Functional Equations

A. Tsutsumi·S. Haruki
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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.Światak. 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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BibTeXRIS

A. Tsutsumi, S. Haruki. 1994-09-21. On an Application of Hypoellipticity to Solutions of Functional Equations. https://arxiv.org/abs/funct-an/9409002

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