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Mathematics of the USSR-Izvestiya, 1977, Volume 11, Issue 1, Pages 205–218
DOI: https://doi.org/10.1070/IM1977v011n01ABEH001706
(Mi im1798)
 

This article is cited in 19 scientific papers (total in 19 papers)

Representation of measurable functions by series in the Faber–Schauder system, and universal series

V. G. Krotov
References:
Abstract: In this work criteria are established for various types of universal series in the Faber–Schauder system of functions. By means of these criteria the maximal speed of decrease is established for coefficients of universal series in this system, and existence is proved for continuous functions with guaranteed (and best possible) smoothness in terms of moduli of continuity whose basis expansions in the Faber–Schauder system are universal in some sense or other. Convergence almost everywhere as well as convergence in integral “metrics” is considered.
Bibliography: 11 titles.
Received: 19.12.1973
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1977, Volume 41, Issue 1, Pages 215–229
Bibliographic databases:
UDC: 517.5
MSC: 28A20, 42A56
Language: English
Original paper language: Russian
Citation: V. G. Krotov, “Representation of measurable functions by series in the Faber–Schauder system, and universal series”, Izv. Akad. Nauk SSSR Ser. Mat., 41:1 (1977), 215–229; Math. USSR-Izv., 11:1 (1977), 205–218
Citation in format AMSBIB
\Bibitem{Kro77}
\by V.~G.~Krotov
\paper Representation of measurable functions by series in the Faber--Schauder system, and universal series
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 1
\pages 215--229
\mathnet{http://mi.mathnet.ru/im1798}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=438033}
\zmath{https://zbmath.org/?q=an:0376.42015|0395.42010}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 1
\pages 205--218
\crossref{https://doi.org/10.1070/IM1977v011n01ABEH001706}
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  • https://doi.org/10.1070/IM1977v011n01ABEH001706
  • https://www.mathnet.ru/eng/im/v41/i1/p215
  • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:515
    Russian version PDF:142
    English version PDF:16
    References:45
    First page:1
     
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