Universality of Composition Operators and Applications to Holomorphic Dynamics

2016/03/03 by Andreas Jung, Jung, Andreas
Mathematics · #Algebraic and Geometric Analysis #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #math.CV #msc:30K20 #msc:37F10 #msc:47A16

paper · pdf · doi:10.48550/arxiv.1603.01091

arxiv created 2016/03/03 · arxiv updated 2016/03/04

Abstract

By investigating which level of universality composition operators C_f can have, where the symbol f is given by the restriction of a transcendental entire function to suitable parts of the Fatou set of f, this work combines the theory of dynamics of continuous linear operators on spaces of holomorphic functions with the theory of non-linear complex dynamics on the complex plane.

Related

• Interactions between Universal Composition Operators and Complex Dynamics
• Dynamics of composition operators on spaces of holomorphic functions on plane domains
• Universal sequences of composition operators
• Universal composition operators
• Universality arising from invertible weighted composition operators