Representable Functions on the Unit Ball of a Banach Space

被引：1
|
作者：
Pinasco, Damian [1 ,2 ]
机构：
[1] Univ Torcuato Tella, Dept Matemat & Estadist, RA-2177 Buenos Aires, DF, Argentina
[2] Consejo Nacl Invest Cient & Tecn, RA-1033 Buenos Aires, DF, Argentina
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2011年 / 8卷 / 03期
关键词：
Integral representation; holomorphic functions; Cauchy integral formula; Wiener measures; HOLOMORPHIC-FUNCTIONS; EXTENSION;
D O I：
10.1007/s00009-010-0093-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we treat the problem of integral representation of analytic functions over the unit ball of a complex Banach space X using the theory of abstract Wiener spaces. We define the class of representable functions on the unit ball of X and prove that this set of functions is related with the classes of integral k-homogeneous polynomials, integral holomorphic functions and also with the set of L (p) -representable functions on a Banach space.
引用
收藏
页码：383 / 398
页数：16
相关论文
共 50 条
  • [1] Representable Functions on the Unit Ball of a Banach Space
    Damián Pinasco
    [J]. Mediterranean Journal of Mathematics, 2011, 8 : 383 - 398
  • [2] BLOCH FUNCTIONS ON THE UNIT BALL OF A BANACH SPACE
    Miralles, Alejandro
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149 (04) : 1459 - 1470
  • [3] COVEING UNIT BALL IN A BANACH SPACE
    CONNETT, J
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1973, 7 (NOV): : 291 - 294
  • [4] COVERING UNIT BALL IN A BANACH SPACE
    CONNETT, JE
    [J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 18 (06): : 954 - &
  • [5] THICK COVERINGS FOR THE UNIT BALL OF A BANACH SPACE
    Castillo, Jesus M. F.
    Papini, P. L.
    Simoes, Marilda
    [J]. HOUSTON JOURNAL OF MATHEMATICS, 2015, 41 (01): : 177 - 186
  • [6] ON EXTREMAL POINTS OF THE UNIT BALL IN THE BANACH-SPACE OF LIPSCHITZ CONTINUOUS-FUNCTIONS
    ROLEWICZ, S
    [J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1986, 41 : 95 - 98
  • [7] Diametral notions for elements of the unit ball of a Banach space
    Martin, Miguel
    Perreau, Yoel
    Zoca, Abraham Rueda
    [J]. DISSERTATIONES MATHEMATICAE, 2024, 594 : 1 - 61
  • [8] Order unit space of type In with Banach ball property
    Berdikulov, MA
    [J]. ALGEBRA AND OPERATOR THEORY, 1998, : 183 - 186
  • [9] A new Banach space with Valdivia dual unit ball
    Ondřej F. K. Kalenda
    [J]. Israel Journal of Mathematics, 2002, 131 : 139 - 147
  • [10] Plasticity of the unit ball of a strictly convex Banach space
    Cascales, B.
    Kadets, V.
    Orihuela, J.
    Wingler, E. J.
    [J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2016, 110 (02) : 723 - 727
12345