The quadratic functional equation on groups
Copyright policy )The quadratic functional equation on groups
The quadratic functional equation \[ f(xy)+f(xy^{-1})=2f(x)+2f(y) \] is considered on free groups. The author presents the result on a general solution of the above equation defined on a free group with values in an abelian group. In the proof some results concerning the Jensen functional equation are utilized. Also general solutions of the above equation on free abelian groups and linear groups of \(n\times n\) invertible matrices over the integers are presented. In the paper some results of \textit{S. Kurepa} [Glas. Mat., III. Ser. 6(26), 265--275 (1971; Zbl 0225.39005)] for quadratic functionals are generalized.
- University of Waterloo Canada
Cauchy kernel, free group, Jensen's functional equation, Periodic groups; locally finite groups, Functional equations for functions with more general domains and/or ranges, abelian group, quadratic functional equation
Cauchy kernel, free group, Jensen's functional equation, Periodic groups; locally finite groups, Functional equations for functions with more general domains and/or ranges, abelian group, quadratic functional equation
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