Composition operators on Hardy spaces of a half plane

Details Composition operators on Hardy spaces of a half plane Composition operators on Hardy spaces of a half plane

2009-07-02

arxiv.org/abs/0907.0350v1

Mathematics

Functional Analysis

Scientific paper

We prove that a composition operator is bounded on the Hardy space $H^2$ of
the right half-plane if and only if the inducing map fixes the point at
infinity non-tangentially, and has a finite angular derivative $\lambda$ there.
In this case the norm, essential norm, and spectral radius of the operator are
all equal to $\sqrt{\lambda}$.

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