Mathematisches Seminar

Dr. Andreas Jung (Universität Trier): "Universality of composition operators and applications in complex dynamics"

09.06.2016 von 14:00 bis 15:30

LMS 4 - Raum 325 - Seminarhörsaal

Ein Vortrag im Rahmen des Oberseminars Analysis auf Einladung von Prof. Bergweiler und Dr. Nieß.


Universality of Composition Operators and
Applications in Complex Dynamics

Let D be an open subset of the complex plane and let f be a holomorphic
self-map of D. We consider the composition operator with symbol f, which
is defined as
Cf : H(D) → H(D), Cf(g) := g ° f.
The transform Cf is a continuous linear operator on the Frechet space H(D).
In case that f is an entire function (not a polynomial of degree 0 or 1) and
D is a suitable f-invariant open subset of the Fatou set of f, we investigate
which level of universality the composition operator Cf|D can have, i.e. we
characterize the H(D)-closure of orbits of functions g ∈ H(D) under Cf|D.
Hence, the theory of dynamics of continuous linear operators on spaces of
holomorphic functions is combined with the theory of non-linear complex
dynamics on the complex plane.

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