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Izv. RAN. Ser. Mat., 1998, Volume 62, Issue 5, Pages 187–206 (Mi izv215)  

This article is cited in 11 scientific papers (total in 11 papers)

Properties of expansion systems similar to orthogonal ones

T. P. Lukashenko

M. V. Lomonosov Moscow State University

Abstract: We define expansion systems in a Hilbert space that are similar to orthogonal ones, for which an analogue of Parseval's equality, the extremal property of expansion coefficients, and analogues of the Riesz-Fischer theorem and Bessel's identity (estimating the accuracy of approximation) are valid. In the case when the Hilbert space is the Lebesgue space $L^2$ we prove an analogue of the Men'shov–Rademacher theorem on almost everywhere convergence and analogues of the theorems of Orlicz and Tandori on unconditional convergence. We suggest constructions and examples of non-orthogonal expansion systems similar to orthogonal ones.

DOI: https://doi.org/10.4213/im215

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English version:
Izvestiya: Mathematics, 1998, 62:5, 1035–1054

Bibliographic databases:

MSC: 42C15
Received: 09.10.1996

Citation: T. P. Lukashenko, “Properties of expansion systems similar to orthogonal ones”, Izv. RAN. Ser. Mat., 62:5 (1998), 187–206; Izv. Math., 62:5 (1998), 1035–1054

Citation in format AMSBIB
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\yr 1998
\vol 62
\issue 5
\pages 187--206
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\yr 1998
\vol 62
\issue 5
\pages 1035--1054
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. T. P. Lukashenko, “Analogs of the Kolmogorov–Seliverstov–Plessner theorem for nonorthogonal function systems”, Math. Notes, 67:1 (2000), 69–80  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Napalkov V., “Various Representations of the Space of Analytic Functions and the Problem of the Dual Space Description”, Dokl. Math., 66:3 (2002), 335–337  mathscinet  zmath  isi
    3. Napalkov V., “Integral Transformations of Bergman Weight Spaces”, Dokl. Math., 70:1 (2004), 504–506  mathnet  mathscinet  zmath  isi
    4. Napalkov V.V., Jr., “Analogue of the Fock space”, Integral Transforms and Special Functions, 18:2 (2007), 133–138  crossref  mathscinet  zmath  isi  elib  scopus
    5. V. V. Napalkov (Jr.), “On orthosimilar systems in a space of analytical functions and the problem of describing the dual space”, Ufa Math. J., 3:1 (2011), 30–41  mathnet  mathscinet  zmath
    6. V. V. Napalkov (ml.), “Ob ekvivalentnoi integralnoi norme v sopryazhennom prostranstve”, Ufimsk. matem. zhurn., 3:4 (2011), 122–132  mathnet  mathscinet  zmath
    7. Napalkov V.V., Napalkov Jr. V. V., “Description of the Operator Dual to the Multiplication Operator in Fock Space”, Dokl. Math., 86:3 (2012), 760–762  crossref  mathscinet  zmath  isi  scopus
    8. Napalkov V.V., Napalkov-ml V.V., “Opisanie sopryazhennogo operatora k operatoru umnozheniya v prostranstve foka”, Doklady akademii nauk, 447:2 (2012), 140–140  crossref  mathscinet  zmath  elib
    9. V. V. Napalkov (Jr.), “Orthosimilar expansion systems in space with reproducing kernel”, Ufa Math. J., 5:4 (2013), 88–100  mathnet  crossref  elib
    10. V. V. Galatenko, T. P. Lukashenko, V. A. Sadovnichii, “The condition of almost everywhere convergence for a functional series with a weak analogue of the orthonormality property”, Moscow University Mathematics Bulletin, 71:2 (2016), 61–67  mathnet  crossref  mathscinet  isi
    11. Napalkov V.V., Napalkov Jr. V. V., “On Isomorphism of Reproducing Kernel Hilbert Spaces”, Dokl. Math., 95:3 (2017), 270–272  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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