  We study the exit time $\tau=\tau_{(0,\infty)}$ for 1-dimensional strictly
stable processes and express its Laplace transform at $t^\alpha$ as the Laplace
transform of a positive random variable with explicit density. Consequently,
$\tau$ satisfies some multiplicative convolution relations. For some stable
processes, e.g. for the symmetric $\frac23$-stable process, explicit formulas
for the Laplace transform and the density of $\tau$ are obtained as an
application.
