Inversion of $\alpha$-sine and $\alpha$-cosine transforms on $\mathbb{R}$

Ly Viet Hoang, Evgeny Spodarev

We consider the $\alpha$-sine transform of the form $T_{\alpha }f(y)={\int }_0^{\infty }|\sin (xy){|}^{\alpha }f(x)dx$ for $\alpha >-1$, where $f$ is an integrable function on ${\mathbb{R}}_{+}$. First, the inver…