A Blaschke-type condition for analytic and subharmonic functions and application to contraction operators

Details A Blaschke-type condition for analytic and subharmonic functions and application to contraction operators A Blaschke-type condition for analytic and subharmonic functions and application to contraction operators

2008-04-20

arxiv.org/abs/0804.3208v2

Linear and Complex Analysis, AMS Translations, 2009 Ser.2, V.226, p.37-47

Mathematics

Complex Variables

12 pages, Bibliography 19 items. Added references, corrected typos

Scientific paper

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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