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arXiv · 2102.01592

Solution of the Kac--Bernstein functional equation on Abelian groups in the class of positive functions

G. M. Feldman
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Abstract

The general form of the solutions of the Kac--Bernstein functional equation $$ f(x+y)g(x-y)=f(x)f(y)g(x)g(-y), \ x, y\in X, $$ on an arbitrary Abelian group $X$ in the class of positive functions is obtained. We also study the solutions of this equation in the class of complex-valued functions that do not vanish and satisfy the Hermitian condition.

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G. M. Feldman. 2021-02-02. Solution of the Kac--Bernstein functional equation on Abelian groups in the class of positive functions. https://arxiv.org/abs/2102.01592

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