On a family of integral operators of Hankel type

In this paper we perform an explicit diagonalization of Hankel integral operators $K^{(0)},K^{(1)},K^{(2)},\mathrm{.}\mathrm{.}\mathrm{.}$ It turns out that each of these operators has a simple purely absolutely continuous spectrum filling in the interval $[-1,1]$. This generalizes a result of Kostrykin and Makarov (2008).