A Blaschke-type Condition for Analytic and Subharmonic Functions and Application to Contraction Operators
نویسنده
چکیده
Abstract. Let E be a closed set on the unit circle. We find a Blaschke-type condition, optimal in a sense of the order, on the Riesz measure of a subharmonic function v in the unit disk with a certain growth at the direction of E. In particular case when E is a finite set, and v = log |f | with an analytic function f , our result agrees with the recent one by A. Borichev, L. Golinskii and S. Kupin. An application to contractions close to unitary operators in the Hilbert space is given.
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