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Izv. Akad. Nauk SSSR Ser. Mat., 1947, Volume 11, Issue 4, Pages 363–400 (Mi izv3004)  

This article is cited in 29 scientific papers (total in 29 papers)

On a class of complete orthonormal systems

N. Vilenkin


Full text: PDF file (2338 kB)

Bibliographic databases:
Received: 25.07.1946

Citation: N. Vilenkin, “On a class of complete orthonormal systems”, Izv. Akad. Nauk SSSR Ser. Mat., 11:4 (1947), 363–400

Citation in format AMSBIB
\Bibitem{Vil47}
\by N.~Vilenkin
\paper On a class of complete
orthonormal systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1947
\vol 11
\issue 4
\pages 363--400
\mathnet{http://mi.mathnet.ru/izv3004}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=22560}
\zmath{https://zbmath.org/?q=an:0125.34304|0036.35601}


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  • http://mi.mathnet.ru/eng/izv/v11/i4/p363

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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. M. Zubakin, “K teorii polnykh multiplikativnykh periodicheskikh ortonormirovannykh sistem”, UMN, 24:6(150) (1969), 187–188  mathnet  mathscinet  zmath
    2. S. L. Blyumin, B. D. Kotlyar, “Hilbert–Schmidt operators and the absolute convergence of fourier series”, Math. USSR-Izv., 4:1 (1970), 215–223  mathnet  crossref  mathscinet  zmath
    3. G. A. Akishev, S. T. Makhashev, “On the absolute convergence of Fourier series in the generalized Haar system”, Russian Math. (Iz. VUZ), 44:3 (2000), 6–14  mathnet  mathscinet  zmath  elib
    4. A. I. Rubinshtein, “On best convergence”, Sb. Math., 192:2 (2001), 277–297  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. V. S. Vykhovanets, V. D. Malyugin, “Multiplikativnaya algebra i ee primenenie v logicheskoi obrabotke dannykh”, Probl. upravl., 3 (2004), 67–77  mathnet  elib
    6. G. A. Akishev, “On orders of approximation of function classes by polynomials in the generalized Haar system”, Russian Math. (Iz. VUZ), 2005, no. 3, 11–20  mathnet  mathscinet  zmath  elib
    7. S. S. Volosivets, “Convergence of fourier series with respect to multiplicative systems and the $p$-fluctuation continuity modulus”, Siberian Math. J., 47:2 (2006), 193–208  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    8. G. A. Akishev, “O poryadkakh priblizheniya klassov polinomami po obobschennoi sisteme Khaara”, Sib. elektron. matem. izv., 3 (2006), 92–105  mathnet  mathscinet  zmath
    9. V. S. Vykhovanets, “Algebraic decomposition of discrete functions”, Autom. Remote Control, 67:3 (2006), 361–392  mathnet  crossref  mathscinet  zmath  elib  elib
    10. M. G. Plotnikov, “On Uniqueness Sets for Multiple Walsh Series”, Math. Notes, 81:2 (2007), 234–246  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. G. A. Akishev, “Absolute convergence of Fourier series of superpositions of functions”, Russian Math. (Iz. VUZ), 53:11 (2009), 1–8  mathnet  crossref  mathscinet  zmath  elib
    12. Kazaryan M.L., “Optimalnoe zonnoe kodirovanie tsifrovykh lipshitsevykh signalov posredstvom klassa sistem modifitsirovannykh preobrazovanii khaara”, Telekommunikatsii, 2011, no. 1, 2–10  elib
    13. M. G. Plotnikov, “Coefficients of convergent multiple Walsh-Paley series”, Sb. Math., 203:9 (2012), 1295–1309  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. M. G. Grigoryan, S. A. Sargsyan, “Nonlinear approximation of functions from the class $L^r$ with respect to the Vilenkin system”, Russian Math. (Iz. VUZ), 57:2 (2013), 25–33  mathnet  crossref
    15. M. G. Plotnikov, “Multiple Walsh Series and Zygmund Sets”, Math. Notes, 95:5 (2014), 686–696  mathnet  crossref  crossref  mathscinet  isi  elib
    16. Volosivets S.S., “Wiener Type Theorems For Fourier-Vilenikin Series With Nonnegative Coefficients and Solid Spaces”, Math. Inequal. Appl., 17:4 (2014), 1415–1425  crossref  isi
    17. M. S. Bespalov, “Generating operator for discrete Chrestenson functions”, Problems Inform. Transmission, 51:1 (2015), 37–48  mathnet  crossref  isi  elib
    18. V. I. Shcherbakov, “Divergence of the Fourier series by generalized Haar systems at points of continuity of a function”, Russian Math. (Iz. VUZ), 60:1 (2016), 42–59  mathnet  crossref  isi
    19. S. A. Sargsyan, “On Lebesgue constants of Vilenkin systems”, Uch. zapiski EGU, ser. Fizika i Matematika, 2016, no. 2, 63–66  mathnet
    20. V. I. Scherbakov, “Priznak Dini–Lipshitsa dlya obobschennykh sistem Khaara”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:4 (2016), 435–448  mathnet  crossref  mathscinet  elib
    21. V. I. Shcherbakov, “Majorants of the Dirichlet Kernels and the Dini Pointwise Tests for Generalized Haar Systems”, Math. Notes, 101:3 (2017), 542–565  mathnet  crossref  crossref  mathscinet  isi  elib
    22. Saghatelyan T.M., “On the Pointwise Universality of the Partial Sums of Fourier Series of l-P,P >= 1 Class By Chrestenson - Levy System”, Math. Montisnigri, 40 (2017), 24–35  isi
    23. G. G. Gevorkyan, K. A. Navasardyan, “Uniqueness Theorems for Generalized Haar Systems”, Math. Notes, 104:1 (2018), 10–21  mathnet  crossref  crossref  mathscinet  isi  elib
    24. Grigoryan M.G., Sargsyan S.A., “Almost Everywhere Convergence of Greedy Algorithm With Respect to Vilenkin System”, J. Contemp. Math. Anal.-Armen. Aca., 53:6 (2018), 331–345  crossref  isi
    25. Yu. A. Farkov, “Diskretnye veivlet-preobrazovaniya v analize Uolsha”, Materialy mezhdunarodnoi konferentsii«InternationalConference onMathematicalModellinginAppliedSciences, ICMMAS-17», Sankt-Peterburgskii politekhnicheskii universitet,2428 iyulya2017 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 160, VINITI RAN, M., 2019, 126–136  mathnet  mathscinet
    26. V. I. Scherbakov, “Sravneniya V- i S-priznakov Dini. Kontrprimery na simmetrichnye priznaki Dini po obobschennym sistemam Khaara i Uolsha”, Izv. vuzov. Matem., 2019, no. 9, 73–95  mathnet  crossref
    27. S. M. Voronov, “Some convergence tests for Fourier series with respect to Vilenkin system in the case of unbounded $p_k$”, Moscow University Mathematics Bulletin, 74:5 (2019), 195–197  mathnet  crossref  mathscinet  isi
    28. Kholshchevnikova N., “the Union Problem and the Category Problem of Sets of Uniqueness in the Theory of Orthogonal Series”, Real Anal. Exch., 44:1 (2019), 65–76  crossref  isi
    29. S. M. Voronov, “Analogue of the Hardy–Littlewood criterion for Fourier series over Vilenkin system in the case of unbounded $p_k$”, Moscow University Mathematics Bulletin, 75:2 (2020), 80–82  mathnet  crossref  isi
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