UNCONDITIONAL BASES OF REPRODUCING KERNELS IN HILBERT SPACES OF ENTIRE FUNCTIONS

被引：9
|
作者：
Isaev, K. P. [1 ]
Yulmukhametov, R. S. [1 ]
机构：
[1] RAS, USC, Inst Math, Chernyshevsky Str 112, Ufa 450008, Russia
来源：
UFA MATHEMATICAL JOURNAL | 2013年 / 5卷 / 03期
关键词：
Hilbert spaces; entire functions; reproducing kernels; unconditional bases;
D O I：
10.13108/2013-5-3-67
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the existence of unconditional bases of reproducing kernels in a functional Hilbert space of entire functions. It is proved that under certain conditions, unconditional bases of reproducing kernels do not exist. It is shown that in particular spaces, some known theorems on the absence of unconditional bases are the consequences of these results.
引用
收藏
页码：67 / 76
页数：10
相关论文
共 50 条
  • [1] On Hilbert Spaces of Entire Functions with Unconditional Bases of Reproducing Kernels
    K. P. Isaev
    R. S. Yulmukhametov
    Lobachevskii Journal of Mathematics, 2019, 40 : 1283 - 1294
  • [2] On Hilbert Spaces of Entire Functions with Unconditional Bases of Reproducing Kernels
    Isaev, K. P.
    Yulmukhametov, R. S.
    LOBACHEVSKII JOURNAL OF MATHEMATICS, 2019, 40 (09) : 1283 - 1294
  • [3] On a Sufficient Condition for the Existence of Unconditional Bases of Reproducing Kernels in Hilbert Spaces of Entire Functions
    Isaev, K. P.
    Yulmukhametov, R. S.
    LOBACHEVSKII JOURNAL OF MATHEMATICS, 2021, 42 (06) : 1154 - 1165
  • [4] On a Sufficient Condition for the Existence of Unconditional Bases of Reproducing Kernels in Hilbert Spaces of Entire Functions
    K. P. Isaev
    R. S. Yulmukhametov
    Lobachevskii Journal of Mathematics, 2021, 42 : 1154 - 1165
  • [5] Necessary Condition for the Existence of Unconditional Bases of Reproducing Kernels for Hilbert Spaces of Entire Functions
    Isaev K.P.
    Lutsenko A.V.
    Yulmukhametov R.S.
    Journal of Mathematical Sciences, 2021, 257 (5) : 662 - 672
  • [6] EQUIVALENT CONDITIONS FOR THE EXISTENCE OF UNCONDITIONAL BASES OF REPRODUCING KERNELS IN SPACES OF ENTIRE FUNCTIONS
    Isaev, K. P.
    Yulmukhametov, R. S.
    PROBLEMY ANALIZA-ISSUES OF ANALYSIS, 2021, 10 (03): : 41 - 52
  • [7] Equivalent Norms in Hilbert Spaces with Unconditional Bases of Reproducing Kernels
    Isaev K.P.
    Trunov K.V.
    Yulmukhametov R.S.
    Journal of Mathematical Sciences, 2020, 250 (2) : 310 - 321
  • [8] GEOMETRY OF RADIAL HILBERT SPACES WITH UNCONDITIONAL BASES OF REPRODUCING KERNELS
    Isaev, K. P.
    Yulmukhametov, R. S.
    UFA MATHEMATICAL JOURNAL, 2020, 12 (04): : 55 - 63
  • [9] ESTIMATES FOR REPRODUCING KERNELS IN WEIGHTED HILBERT SPACES OF ENTIRE FUNCTIONS
    HANTLER, SL
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 21 (07): : A593 - A593
  • [10] On the theory of unconditional bases of Hilbert spaces formed by entire vector-functions
    Gubreev, Gennadiy
    Tarasenko, Anna
    BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2018, 24 (01): : 269 - 278
12345