  In this paper, we study Feynman-Kac semigroups of symmetric $\alpha$-stable
processes with supercritical killing potentials belonging to a large class of
functions containing functions of the form $b|x|^{-\beta}$, where $b>0$ and
$\beta>\alpha$. We obtain two-sided estimates on the densities $p(t, x, y)$ of
these semigroups for all $t>0$, along with estimates for the corresponding
Green functions.
