What do composition operators
know about inner functions?
Joel H. Shapiro
Monatshefte für Mathematik
130 (2000), 57--70.
Abstract: This
paper gives several different ways in which operator norms characterize
those composition operators that arise from holomorphic self-maps
of the unit disc that are inner functions.
The setting is the Hardy space H^2 of the
disc, and the key result is a characterization of inner functions
in terms of the asymptotic behavior of the Nevanlinna counting
function.
When the inducing map does not fix the origin
there is an interesting surprise!
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