  It is shown that if a probability measure $\nu$ is supported on a closed
subset of $(0,\infty)$, that is, its support is bounded away from zero, then
the free multiplicative convolution of $\nu$ and the semicircle law is
absolutely continuous with respect to the Lebesgue measure. For the proof, a
result concerning the Hadamard product of a deterministic matrix and a scaled
Wigner matrix is proved and subsequently used. As a byproduct, a result,
showing that the limiting spectral distribution of the Hadamard product is same
as that of a symmetric random matrix with entries from a mean zero stationary
Gaussian process, is obtained.
