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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: 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?)

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  • [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)
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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0942634-7
PII: S 0002-9939(1989)0942634-7
Article copyright: © Copyright 1989 American Mathematical Society