M. D. Contreras, S. Díaz-Madrigal, P. Gumenyuk

Infinitesimal generators of semigroups with prescribed boundary fixed points

Analysis and Mathematical Physics, 10(3):article 36, 2020.
DOI: 10.1007/s13324-020-00378-z

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 $\mathbb D$.

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