The numerical ranges of
automorphic composition operators

Paul S. Bourdon and Joel H. Shapiro

J. Math. Analysis and Appl., 251 (2000), 839-854.

Abstract: We 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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