Evolution equations for Lévy stable processes (Q1964577)

Let \(p(\cdot,t)\) be the probability density of the distribution of some stable Lévy process evaluated at time \(t>0\). This gives rise to a convolution semigroup which satisfies the so-called `evolution equation' \({\partial p\over \partial t}=Lp(\cdot,t),\) where \(L\) is the infinitesimal generator of the process. Explicit (known) formulas for \(L\) are presented.