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General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series


Abstract

We prove that the classical Menshov-Rademacher, Orlicz, and Tandori theorems remain true for orthogonal series given in the direct integrals of measurable collections of Hilbert spaces. In particular, these theorems are true for the spaces $L_{2}(X,d\mu;H)$ of vector-valued functions, where $(X,\mu)$ is an arbitrary measure space, and $H$ is a real or complex Hilbert space of an arbitrary dimension.


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Article Information

TitleGeneral forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series
SourceMethods Funct. Anal. Topology, Vol. 17 (2011), no. 4, 330-340
MathSciNet MR2907361
CopyrightThe Author(s) 2011 (CC BY-SA)

Authors Information

Vladimir A. Mikhailets
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

Aleksandr A. Murach
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine 


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Citation Example

Vladimir A. Mikhailets and Aleksandr A. Murach, General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series, Methods Funct. Anal. Topology 17 (2011), no. 4, 330-340.


BibTex

@article {MFAT608,
    AUTHOR = {Mikhailets, Vladimir A. and Murach, Aleksandr A.},
     TITLE = {General forms of  the Menshov-Rademacher, Orlicz, and Tandori theorems  on orthogonal series},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {17},
      YEAR = {2011},
    NUMBER = {4},
     PAGES = {330-340},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=608},
}


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