Affiliation:
1. Department of Statistics, Purdue University, West Lafayette, Indiana 47907, USA
Abstract
A functional equation of the formϕ1(x+y)+ϕ2(x−y)=∑inαi(x)βi(y), where functionsϕ1,ϕ2,αi,βi,i=1,…,nare 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.
Funder
National Science Foundation
Subject
Mathematics (miscellaneous)
Cited by
8 articles.
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1. Exponential Rationals;Results in Mathematics;2023-12-02
2. Klee's Trigonometry Problem;The American Mathematical Monthly;2003-12
3. Wilson’s functional equation for vector and matrix functions;Proceedings of the American Mathematical Society;1997
4. Regularization and general methods in the theory of functional equations;Aequationes Mathematicae;1996-02
5. Generalized sine equations, II;Aequationes Mathematicae;1995-02