Infinitesimal generators of semigroups with prescribed boundary fixed points

Abstract

We study infinitesimal generators of one-parameter semigroups in the unit disk D having prescribed boundary regular fixed points. Using an explicit representation of such infinitesimal generators in combination with Krein-Milman Theory we obtain new sharp inequalities relating spectral values at the fixed points with other important quantities having dynamical meaning. We also give a new proof of the classical Cowen-Pommerenke inequalities for univalent self-maps of D.