Generalizations of the functional equation of the mean sun |
Abstract: Two generalizations U(λ+μ) y(ν)=U(λ)y(μ+ν)
(for all λ,μ,ν in A ) of the functional equation of the mean sun are studied, where (A,+) is an Abelian group, K is a field, n is a positive integer, and both y: A→ K^{n} and U: A→ GL(n,k) (or U: A→ M_{n}(k) in the second case) are unknown functions, which will be determined by the equation.
Generalizations of the functional equation of the mean sun |