Functional equations on abelian groups with involution
The author investigates generalizations of several functional equations such as d'Alembert's, Wilson's, Jensen's and the functional equation of quadratic functions. The main point is that he replaces terms of the form \(x-y\) by \(x+ \sigma (y)\), where \(\sigma\) is an involution. Moreover a general framework is used which is interesting for itself. The main tool is the notion of a \(K\)-spherical function, where \(K\) is a compact transformation group of a topological group. The paper is very interesting, unifies and generalizes earlier results and shows new perspectives in the considered area.
functional equation of quadratic functions
scientific article; zbMATH DE number 1053605
scientific article