Aleksandrov-Clark measures and semigroups of analytic functions in the unit disc

In this paper we prove a formula describing the infinitesimal generator of a contin- uous semigroup ('t) of holomorphic self-maps of the unit disc with respect to a boundary regular fixed point. The result is based on Aleksandrov-Clark measures techniques. In particular we prove that the Aleksandrov-Clark measure of ('t) at a boundary regular fixed point is dierentiable (in the weak ⁄ -topology) with respect to t.