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Reformulation of some functional equations in the space of Gevrey distributions and regularity of solutions

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Summary.

We reformulate several well-known functional equations including Cauchy equation, Pexider equation, Jensen equation, Pompeiu equation and their generalized forms as equations for Gevrey distributions and show that every solution of each functional equation in the space of Gevrey distributions is Gevrey differentiable.

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Authors and Affiliations

  1. Department of Mathematics, Sogang University, Seoul 121-742, Korea, e-mail: sychung@ccs.sogang.ac.kr , , , , , , KR

    S.-Y. Chung

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  1. S.-Y. Chung
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Received: May 5, 1998; revised version: April 12, 1999.

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Chung, SY. Reformulation of some functional equations in the space of Gevrey distributions and regularity of solutions. Aequ. math. 59, 108–123 (2000). https://doi.org/10.1007/PL00000118

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  • DOI: https://doi.org/10.1007/PL00000118

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