  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.vWe also give a new proof of the classical Cowen-Pommerenke
inequalities for univalent self-maps of $\mathbb D$.
