Solution of Functional Equations Related to Elliptic Functions

Resumo

Functional equations of the form f(x + y)g(x − y) = Σ_j=1ⁿ α_j(x)β_j (y) as well as of the form f₁(x + z)f₂(y + z)f₃(x + y − z) = Σ_j=1^mφ_j(x, y)ψ_j (z) are solved for unknown entire functions f, g,α_j, β_j: ℂ → ℂ and f₁, f₂, f₃, ψ_j: ℂ → ℂ, φ_j: ℂ² → ℂ in the cases of n = 3 and m = 4.