The Cauchy functional equations in distributions
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- by E. L. Koh PDF
- Proc. Amer. Math. Soc. 106 (1989), 641-646 Request permission
Abstract:
The Pompeiu functional equation is defined by Neagu for Schwartz distributions. His method is extended to the four Cauchy functional equations by means of two new operators ${Q^*}$ and ${R^*}$ on $\mathcal {D}’(I)$. The Cauchy equations in distributions reduce to the classical equations when the solutions are regular distributions, i.e. locally integrable functions.References
- M. Neagu, About the Pompeiu equation in distributions, Inst. Politehn. Traian Vuia Timişoara Lucrăr. Sem. Mat. Fiz. May (1984), 62–66 (English, with Romanian summary). MR 783941
- I. Fenyő, On the general solution of a functional equation in the domain of distributions, Aequationes Math. 3 (1969), 236–246. MR 611691, DOI 10.1007/BF01817444
- J. Aczél, Lectures on functional equations and their applications, Mathematics in Science and Engineering, Vol. 19, Academic Press, New York-London, 1966. Translated by Scripta Technica, Inc. Supplemented by the author. Edited by Hansjorg Oser. MR 0208210
- Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, IX-X, Hermann, Paris, 1966 (French). Nouvelle édition, entiérement corrigée, refondue et augmentée. MR 0209834
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 641-646
- MSC: Primary 39B20; Secondary 46F10
- DOI: https://doi.org/10.1090/S0002-9939-1989-0942634-7
- MathSciNet review: 942634