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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
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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Article copyright: © Copyright 1989 American Mathematical Society