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

2021/02/02 by Feldman, G. M.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2102.01592

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∈ 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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