English

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

Classical Analysis and ODEs 2021-02-03 v1 Group Theory

Abstract

The general form of the solutions of the Kac--Bernstein functional equation f(x+y)g(xy)=f(x)f(y)g(x)g(y), x,yX, f(x+y)g(x-y)=f(x)f(y)g(x)g(-y), \ x, y\in X, on an arbitrary Abelian group XX 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.

Keywords

Cite

@article{arxiv.2102.01592,
  title  = {Solution of the Kac--Bernstein functional equation on Abelian groups in the class of positive functions},
  author = {G. M. Feldman},
  journal= {arXiv preprint arXiv:2102.01592},
  year   = {2021}
}