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

被引：5

作者：

Favorov, Sergey ^{[1
]}

Golinskii, Leonid ^{[2
]}

机构：

[1] Karazin Natl Univ, Sch Math, UA-61077 Kharkov, Ukraine

[2] Kharkov Low Temp Phys & Engn Inst, Div Math, UA-61103 Kharkov, Ukraine

来源：

COMPUTATIONAL METHODS AND FUNCTION THEORY | 2012年 / 12卷 / 01期

关键词：

Subharmonic functions; Riesz measure; canonical products; Minkowski dimension; Weierstrass prime factor;

D O I：

10.1007/BF03321819

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：151 / 166

页数：16

共 10 条

[1] Blaschke-Type Conditions for Analytic and Subharmonic Functions in the Unit Disk: Local Analogs and Inverse Problems
Sergey Favorov
Leonid Golinskii
Computational Methods and Function Theory, 2012, 12 : 151 - 166
[2] A characterization of random analytic functions satisfying Blaschke-type conditions
Duan, Yongjiang
Fang, Xiang
Zhan, Na
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2024, 67 (03): : 670 - 679
[3] ON A BLASCHKE-TYPE CONDITION FOR THE ZEROS OF DERIVATIVES OF R. NEVANLINNA CLASS FUNCTIONS IN THE DISK
Shamoyan, F. A.
ST PETERSBURG MATHEMATICAL JOURNAL, 2024, : 1063 - 1072
[4] ANALOGS OF RADIAL UNIQUENESS THEOREMS FOR SUBHARMONIC FUNCTIONS IN THE UNIT DISK
BERMAN, RD
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1984, 29 (FEB): : 103 - 112
[5] LOCAL HARMONIC MAJORANTS OF FUNCTIONS SUBHARMONIC IN UNIT DISK
GAUTHIER, PM
HENGARTN.W
JOURNAL D ANALYSE MATHEMATIQUE, 1973, 26 : 405 - 412
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Kheifets, Alexander
MATHEMATISCHE NACHRICHTEN, 2009, 282 (11) : 1513 - 1536
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Fournier, R
Ruscheweyh, S
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (11) : 3287 - 3294
[8] A Blaschke-type condition for analytic functions on finitely connected domains. Applications to complex perturbations of a finite-band selfadjoint operator
Golinskii, L.
Kupin, S.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 389 (02) : 705 - 712
[9] Interpolation sequences for the class of functions of finite η-type analytic in the unit disk
Vynnyts'kyi B.V.
Sheparovych I.B.
Ukrainian Mathematical Journal, 2004, 56 (3) : 520 - 526
[10] SHARP WEAK-TYPE INEQUALITIES FOR ANALYTIC-FUNCTIONS ON THE UNIT DISK
TOMASZEWSKI, B
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1986, 18 : 355 - 358

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