  The truncated Hilbert transform with overlap $H_T$ is an operator that arises
in tomographic reconstruction from limited data, more precisely in the method
of Differentiated Back-Projection (DBP). Recent work [1] has shown that the
singular values of this operator accumulate at both zero and one. To better
understand the properties of the operator and, in particular, the ill-posedness
of the inverse problem associated with it, it is of interest to know the rates
at which the singular values approach zero and one. In this paper, we exploit
the property that $H_T$ commutes with a second-order differential operator
$L_S$ and the global asymptotic behavior of its eigenfunctions to find the
asymptotics of the singular values and singular functions of $H_T$.
