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The Cauchy functional equations in distributions


Author: E. L. Koh
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
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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" Timisoara. Lucrar. Sem. Mat. Fiz. (1984) May, 62-66. MR 783941 (86i:46044)
  • [2] I. Fenyö, 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. Aczel, Lectures on functional equations and their applications, Academic Press, New York, 1966. MR 0208210 (34:8020)
  • [4] L. Schwartz, Théorie des Distributions, Hermann, Paris, 1966. MR 0209834 (35:730)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0942634-7
Article copyright: © Copyright 1989 American Mathematical Society

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