  We characterize the subexponential densities on $(0,\infty)$ for compound
Poisson distributions on $[0,\infty)$ with absolutely continuous L\'evy
measures. As a corollary, we show that the class of all subexponential
probability density functions on $\mathbb R_+$ is closed under generalized
convolution roots of compound Poisson sums. Moreover, we give an application to
the subexponential density on $(0,\infty)$ for the distribution of the supremum
of a random walk.
