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Matematicheskie Zametki, 1969, Volume 6, Issue 6, Pages 737–747 (Mi mzm6982)  
This article is cited in 7 scientific papers (total in 7 papers)

On the extension of a sequence of functions to a complete orthonormal system

A. M. Olevskii

Moscow Institute of Electronic Engineering
Full-text PDF (684 kB) Citations (7)
Abstract: Necessary and sufficient conditions for extending a sequence of functions to a complete orthonormal system on a larger set are indicated. As an application of the extension problem, a description of the space of coefficients of orthogonal series in a complete bounded system, converging on sets of positive measure, is given.
Received: 21.02.1969
English version:
Mathematical Notes, 1969, Volume 6, Issue 6, Pages 908–913
DOI: https://doi.org/10.1007/BF01146412
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: A. M. Olevskii, “On the extension of a sequence of functions to a complete orthonormal system”, Mat. Zametki, 6:6 (1969), 737–747; Math. Notes, 6:6 (1969), 908–913
Citation in format AMSBIB
\Bibitem{Ole69}
\by A.~M.~Olevskii
\paper On the extension of a~sequence of functions to a~complete orthonormal system
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 6
\pages 737--747
\mathnet{http://mi.mathnet.ru/mzm6982}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=262762}
\zmath{https://zbmath.org/?q=an:0192.42901}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 6
\pages 908--913
\crossref{https://doi.org/10.1007/BF01146412}
Linking options:
  • https://www.mathnet.ru/eng/mzm6982
  • https://www.mathnet.ru/eng/mzm/v6/i6/p737
    • This publication is cited in the following 7 articles:
    1. P. A. Terekhin, “On Bessel Systems in a Banach Space”, Math. Notes, 91:2 (2012), 272–282  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. M. I. Ismailov, “Gilbertovy obobscheniya b-besselevykh sistem”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 11:3(2) (2011), 3–10  mathnet  crossref  elib
    3. P. A. Terekhin, “Proektsionnye kharakteristiki besselevykh sistem”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 9:1 (2009), 44–51  mathnet  crossref  elib
    4. B. S. Kashin, T. Yu. Kulikova, “A Note on the Description of Frames of General Form”, Math. Notes, 72:6 (2002), 863–867  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Michiel Hazewinkel, Encyclopaedia of Mathematics, 1991, 1  crossref
    6. V. I. Ivanov, “Approximation in Lp by polynomials in the Walsh system”, Math. USSR-Sb., 62:2 (1989), 385–402  mathnet  crossref  mathscinet  zmath
    7. A. S. Krantsberg, “On divergent Fourier series in orthogonal systems”, Math. USSR-Sb., 22:4 (1974), 547–560  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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