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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 1, Pages 215–229 (Mi izv1798)  

This article is cited in 9 scientific papers (total in 9 papers)

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

V. G. Krotov

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.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:1, 205–218

Bibliographic databases:

UDC: 517.5
MSC: 28A20, 42A56
Received: 19.12.1973

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
\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
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 1
\pages 205--218

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    This publication is cited in the following articles:
    1. A. A. Talalyan, R. I. Ovsepian, “The representation theorems of D. E. Men'shov and their impact on the development of the metric theory of functions”, Russian Math. Surveys, 47:5 (1992), 13–47  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. M. A. Nalbandyan, “Representation of measurable functions by series with respect to Walsh subsystems”, Russian Math. (Iz. VUZ), 53:10 (2009), 45–56  mathnet  crossref  mathscinet  zmath  elib
    3. V. I. Filippov, “Representation systems obtained using translates and dilates of a single function in multidimensional spaces $E_{\varphi}$”, Izv. Math., 76:6 (2012), 1257–1270  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. M. G. Grigoryan, V. G. Krotov, “Luzin's Correction Theorem and the Coefficients of Fourier Expansions in the Faber–Schauder System”, Math. Notes, 93:2 (2013), 217–223  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Grigoryan M.G. Sargsyan A.A., “On the universal function for the class L p [0,1], p (0,1)”, J. Funct. Anal., 270:8 (2016), 3111–3133  crossref  mathscinet  zmath  isi  elib  scopus
    6. Sargsyan A. Grigoryan M., “Universal Function For a Weighted Space l-Mu(1) [0,1]”, Positivity, 21:4 (2017), 1457–1482  crossref  isi
    7. Grigoryan M. Grigoryan T. Sargsyan A., “On the Universal Function For Weighted Spaces l-Mu(P)[0,1], P >= 1”, Banach J. Math. Anal., 12:1 (2018), 104–125  crossref  isi
    8. M. G. Grigoryan, A. A. Sargsyan, “The Fourier–Faber–Schauder series unconditionally divergent in measure”, Siberian Math. J., 59:5 (2018), 835–842  mathnet  crossref  crossref  isi
    9. Grigoryan M., Sargsyan A., “On the Structure of Universal Functions For Classes l-P[0,1)(2), P Is An Element of (0,1), With Respect to the Double Walsh System”, Banach J. Math. Anal., 13:3 (2019), 647–674  crossref  isi
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