The numerical ranges of
Paul S. Bourdon and Joel H. Shapiro
automorphic composition operators
J. Math. Analysis and Appl.,
251 (2000), 839-854.
investigate the shape of the numerical range for composition
operators induced on the Hardy space H^2 by conformal automorphisms
of the unit disc. We show that usually, but not always, such
operators have numerical ranges whose closures are discs centered
at the origin. Surprising open questions arise from our investigation.
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