sine addition law

Integral of an extension of the sine addition formula

In this paper, we determine the continuous solutions of the integral functional equation of Stetkær's extension of the sine addition law $\int_{G}f(xyt)d\mu(t)=f(x)\chi_1(y)+\chi_2(x)f(y)$, $x,y\in G$, where $f\colon G\rightarrow \mathbb{C}$, $G$ is a locally compact Hausdorff group, $\mu$ is a regular, compactly supported, complex-valued Borel measure on $G$ and $\chi_1$, $\chi_2$ are fixed characters on $G$.