Arguments of Zero Sets in the Dirichlet Space

被引：0
|
作者：
Mashreghi, Javad [1 ]
Ransford, Thomas [1 ]
Shabankhah, Mahmood [1 ]
机构：
[1] Univ Laval, Dept Math & Stat, Quebec City, PQ G1V 0A6, Canada
来源：
HILBERT SPACES OF ANALYTIC FUNCTIONS | 2010年 / 51卷
关键词：
Zero sets; Dirichlet space; Carleson sets; Blaschke sets;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We characterize the unimodular sequences (e(i theta n))(n >= 1) such that (r(n)e(i theta n))(n >= 1) is a zero set for the Dirichlet space for every positive Blaschke sequence (r(n))(n >= 1). The principal tool is a characterization of Carleson sets in terms of their convergent subsequences.
引用
收藏
页码：143 / 148
页数：6
相关论文
共 50 条
  • [1] On Zero Sets in the Dirichlet Space
    Karim Kellay
    Javad Mashreghi
    Journal of Geometric Analysis, 2012, 22 : 1055 - 1070
  • [2] On Zero Sets in the Dirichlet Space
    Kellay, Karim
    Mashreghi, Javad
    JOURNAL OF GEOMETRIC ANALYSIS, 2012, 22 (04) : 1055 - 1070
  • [3] Zero sets and uniqueness sets with one cluster point for the Dirichlet space
    Mashreghi, Javad
    Shabankhah, Mahmood
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 357 (02) : 498 - 503
  • [4] Blaschke Products and Zero Sets in Weighted Dirichlet Spaces
    H. Bahajji-El Idrissi
    O. El-Fallah
    Potential Analysis, 2020, 53 : 1299 - 1316
  • [5] Blaschke condition and zero sets in weighted Dirichlet spaces
    Guillot, Dominique
    ARKIV FOR MATEMATIK, 2012, 50 (02): : 269 - 278
  • [6] Blaschke Products and Zero Sets in Weighted Dirichlet Spaces
    Idrissi, H. Bahajji-El
    El-Fallah, O.
    POTENTIAL ANALYSIS, 2020, 53 (04) : 1299 - 1316
  • [7] Level sets and composition operators on the Dirichlet space
    El-Fallah, O.
    Kellay, K.
    Shabankhah, M.
    Youssfi, H.
    JOURNAL OF FUNCTIONAL ANALYSIS, 2011, 260 (06) : 1721 - 1733
  • [8] Blaschke sequences and zero sets for Dirichlet spaces with superharmonic weights
    Bao, Guanlong
    Mashreghi, Javad
    Wang, Zipeng
    Wulan, Hasi
    MATHEMATISCHE ZEITSCHRIFT, 2025, 309 (03)
  • [9] Inner functions as multipliers and zero sets in weighted Dirichlet spaces
    Yang, Liu
    GEORGIAN MATHEMATICAL JOURNAL, 2020, 27 (04) : 655 - 660
  • [10] ZERO SETS, INTERPOLATING-SEQUENCES, AND CYCLIC VECTORS FOR DIRICHLET SPACES
    CHAN, KC
    SHIELDS, AL
    MICHIGAN MATHEMATICAL JOURNAL, 1992, 39 (02) : 289 - 307
12345