正函数类中阿贝尔群上Kac-Bernstein函数方程的解
Solution of the Kac--Bernstein functional equation on Abelian groups in the class of positive functions
摘要：
给出了任意阿贝尔群$X$上Kac-Bernstein函数方程$$ f(x+y)g(x-y)=f(x)f(y)g(x)g(-y), \ x, y\in X, $$在正函数类中解的一般形式.我们还研究了该方程在不为零且满足埃尔米特条件的复值函数类中的解。
英文摘要：
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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