Browsing by Subject "Convexity"

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    Convexity of the Berezin Range
    (Elsevier, 2022) Cowen, Carl C.; Felder, Christopher; Mathematical Sciences, School of Science
    This paper discusses the convexity of the range of the Berezin transform. For a bounded operator T acting on a reproducing kernel Hilbert space H (on a set X), this is the set B(T):={〈Tkˆx,kˆx〉H:x∈X}, where kˆx is the normalized reproducing kernel for H at x∈X. Primarily, we focus on characterizing convexity of this range for a class of composition operators acting on the Hardy space of the unit disk.