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Stability of the Cauchy equation for convolutions

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Summary.

In this paper we prove the lack of superstability of the Cauchy functional equation

$$ F(x * y) = F(x) * F(y) $$

on a semigroup (X, *), where X is a function space with the convolution multiplication *.

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Authors and Affiliations

  1. Pedagogical Academy, Institute of Mathematics, ul. Podchorażych 2, PL-30-084, Kraków, Poland

    Stanisław Siudut

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  1. Stanisław Siudut
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Correspondence to Stanisław Siudut.

Additional information

Manuscript received: November 6, 2002 and, in final form, February 16, 2005.

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Siudut, S. Stability of the Cauchy equation for convolutions. Aequ. math. 71, 201–208 (2006). https://doi.org/10.1007/s00010-005-2798-2

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  • DOI: https://doi.org/10.1007/s00010-005-2798-2

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