The solution of the functional equation of D'Alembert's type for commutative groups

A. L. Rukhin

International Journal of Mathematics and Mathematical Sciences, 1982, vol. 5, 1-21

Abstract:

A functional equation of the form ϕ 1 ( x + y ) + ϕ 2 ( x − y ) = ∑ i n α i ( x ) β i ( y ) , where functions ϕ 1 , ϕ 2 , α i , β i , i = 1 , … , n are defined on a commutative group, is solved. We also obtain conditions for the solutions of this equation to be matrix elements of a finite dimensional representation of the group.

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:848617

DOI: 10.1155/S0161171282000301

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