A system of cosine-sine functional equations on a semigroup generated by its squares

2022/09/20 by Ajebbar, Omar, Elqorachi, Elhoucien
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2209.09571

Abstract

Given a semigroup S generated by its squares, we determine the complex-valued solutions of the following system of cosine-sine functional equations f(xy)=f(x)g₁(y)+g₁(x)f(y)+λ₁² h(x)h(y), x,y∈ S,
h(xy)=h(x)g₂(y)+g₂(x)h(y)+λ₂² f(x)f(y), x,y∈ S, where λ₁,λ₂∈ℂ are given constants and f,g₁,g₂,h:S→ℂ are unknown functions.

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