Infinitesimal generators of semigroups with prescribed boundary fixed points

Abstract

We study infinitesimal generators of one-parameter semigroups in the unit disk $$\mathbb {D}$$ 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 $$\mathbb {D}$$ .