On an application of hypoellipticity to solutions of functional equations
Copyright policy )On an application of hypoellipticity to solutions of functional equations
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.
9 pages, LaTeX
- Osaka Shoin Women's University Japan
- DigiZeitschriften Germany
- Okayama University of Science Japan
functional equations, distributions, hypoellipticity, infinitely often differentiable functions, Continuity and differentiation questions, continuous, Article, Operations with distributions and generalized functions, Functional Analysis (math.FA), Mathematics - Functional Analysis, 510.mathematics, Functional equations for real functions, locally integrable, FOS: Mathematics, Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
functional equations, distributions, hypoellipticity, infinitely often differentiable functions, Continuity and differentiation questions, continuous, Article, Operations with distributions and generalized functions, Functional Analysis (math.FA), Mathematics - Functional Analysis, 510.mathematics, Functional equations for real functions, locally integrable, FOS: Mathematics, Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
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