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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


The Cauchy functional equations in distributions

Author: E. L. Koh
Journal: Proc. Amer. Math. Soc. 106 (1989), 641-646
MSC: Primary 39B20; Secondary 46F10
MathSciNet review: 942634
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] 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 (86i:46044)
  • [2] I. Fenyő, On the general solution of a functional equation in the domain of distributions, Aequationes Math. 3 (1969), 236–246. MR 0611691 (58 #29538)
  • [3] 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 (34 #8020)
  • [4] Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX-X. Nouvelle édition, entiérement corrigée, refondue et augmentée, Hermann, Paris, 1966 (French). MR 0209834 (35 #730)

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Additional Information

PII: S 0002-9939(1989)0942634-7
Article copyright: © Copyright 1989 American Mathematical Society

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