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Universal functions for composition operators with non-automorphic symbol

✍ Scribed by Karl-G. Grosse-Erdmann; Raymond Mortini

Book ID
107526902
Publisher
Springer-Verlag
Year
2009
Tongue
English
Weight
281 KB
Volume
107
Category
Article
ISSN
0021-7670

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Let p ∈ U, Ξ± p (z) := p-z 1-pz (z ∈ U) and let C Ξ± p : H 2 β†’ H 2 be the composition operator induced by the conformal automorphism Ξ± p . In this paper we show that the closure of the numerical range of C Ξ± p , W (C Ξ± p ), is an ellipse with foci at Β±1 and major axis 2 √ 1-|p| 2 .