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Blaschke-Type Conditions for Analytic and Subharmonic Functions in the Unit Disk: Local Analogs and Inverse Problems

Blaschke-Type Conditions for Analytic and Subharmonic Functions in the Unit Disk: Local Analogs... We continue the study of analytic and subharmonic functions in the unit disk of finite order with an arbitrary set of singular points on the unit circle, introduced in [6]. We focus on a local analog of the main result from [6], which is similar to the standard local Blaschke condition for analytic functions bounded in a lune of the unit disk. We also discuss the inverse problem, i.e. the existence of a subharmonic function from this class with a given singular set on the circle and given Riesz measure subject to a certain Blaschke-type condition. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Blaschke-Type Conditions for Analytic and Subharmonic Functions in the Unit Disk: Local Analogs and Inverse Problems

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321819
Publisher site
See Article on Publisher Site

Abstract

We continue the study of analytic and subharmonic functions in the unit disk of finite order with an arbitrary set of singular points on the unit circle, introduced in [6]. We focus on a local analog of the main result from [6], which is similar to the standard local Blaschke condition for analytic functions bounded in a lune of the unit disk. We also discuss the inverse problem, i.e. the existence of a subharmonic function from this class with a given singular set on the circle and given Riesz measure subject to a certain Blaschke-type condition.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Jan 21, 2012

References