Kœnigs Type Starlike and Spirallike Functions
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In this chapter we study linear-fractional models for discrete and continuous semigroups of holomorphic functions on the open unit disk Δ. This study is based on solutions of classical Schröder’s and Abel’s functional equations. It turns out that different problems of the semigroup theory (like the embedding problem, asymptotic behavior and rigidity) closely connected to geometrical properties of the solutions of Schröder’s and Abel’s equations. In order to emphasize more important conceptual issues, we refer the reader to related sources for the proofs of some technical results for discrete time semigroups.
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