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- W2032696397 abstract "For any analytic self-map $psi$ of ${z: |z| < 1}$, J. H. Shapiro has established that the square of the essential norm of the composition operator $C_psi$ on the Hardy Space $H^2$ is precisely $limsup_{|w|rightarrow 1^-}N_psi(w)/(1-|w|)$; where $N_psi$ is the Nevanlinna counting function for $psi$. In this paper we show that this quantity is equal to $limsup_{|a|rightarrow 1^-}(1 - |a|^2)||1/(1 - bar{a}psi)||_{H^2}^2.$ This alternative expression provides a link between the one given by Shapiro and earlier measure-theoretic notions. Applications are given." @default.
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- W2032696397 date "2010-08-18" @default.
- W2032696397 modified "2023-09-27" @default.
- W2032696397 title "On Shapiro's Compactness Criterion for Composition Operators" @default.
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