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

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

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/izv1798} \mathscinet{http://www.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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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. 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
2. M. A. Nalbandyan, “Representation of measurable functions by series with respect to Walsh subsystems”, Russian Math. (Iz. VUZ), 53:10 (2009), 45–56
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
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
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
6. Sargsyan A. Grigoryan M., “Universal Function For a Weighted Space l-Mu(1) [0,1]”, Positivity, 21:4 (2017), 1457–1482
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
8. M. G. Grigoryan, A. A. Sargsyan, “The Fourier–Faber–Schauder series unconditionally divergent in measure”, Siberian Math. J., 59:5 (2018), 835–842
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
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