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Uspekhi Mat. Nauk, 1966, Volume 21, Issue 6(132), Pages 3–82 (Mi umn5939)  

This article is cited in 40 scientific papers (total in 40 papers)

Lacunary series and independent functions

V. F. Gaposhkin


Full text: PDF file (7624 kB)
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English version:
Russian Mathematical Surveys, 1966, 21:6, 1–82

Bibliographic databases:

UDC: 519.2+517.5
MSC: 30B10, 28A20, 40A05
Received: 11.06.1965

Citation: V. F. Gaposhkin, “Lacunary series and independent functions”, Uspekhi Mat. Nauk, 21:6(132) (1966), 3–82; Russian Math. Surveys, 21:6 (1966), 1–82

Citation in format AMSBIB
\Bibitem{Gap66}
\by V.~F.~Gaposhkin
\paper Lacunary series and independent functions
\jour Uspekhi Mat. Nauk
\yr 1966
\vol 21
\issue 6(132)
\pages 3--82
\mathnet{http://mi.mathnet.ru/umn5939}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=206556}
\zmath{https://zbmath.org/?q=an:0178.06903}
\transl
\jour Russian Math. Surveys
\yr 1966
\vol 21
\issue 6
\pages 1--82
\crossref{https://doi.org/10.1070/RM1966v021n06ABEH001196}


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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. V. F. Gaposhkin, “Sistemy vida $\{\varphi_k(n_k{x})\}$, ekvivalentnye sistemam nezavisimykh funktsii”, UMN, 22:1(133) (1967), 184–185  mathnet  mathscinet
    2. V. F. Gaposhkin, “On asymptotically best lacunary systems”, Math. USSR-Izv., 1:5 (1967), 967–982  mathnet  crossref  mathscinet  zmath
    3. V. F. Gaposhkin, “O podsistemakh periodicheskikh multiplikativnykh sistem funktsii”, UMN, 24:4(148) (1969), 191–192  mathnet  mathscinet  zmath
    4. A. S. Vinogradskii, “Boundary properties of surfaces with slowly varying negative curvature”, Math. USSR-Sb., 11:2 (1970), 257–271  mathnet  crossref  mathscinet  zmath
    5. V. F. Gaposhkin, “On the convergence of series of weakly multiplicative systems of functions”, Math. USSR-Sb., 18:3 (1972), 361–372  mathnet  crossref  mathscinet  zmath
    6. L. V. Zhizhiashvili, “Some problems in the theory of simple and multiple trigonometric and orthogonal series”, Russian Math. Surveys, 28:2 (1973), 65–127  mathnet  crossref  mathscinet  zmath
    7. E. A. Bredikhina, “On the Lebesgue constants of some classes of almost periodic functions”, Math. USSR-Sb., 25:4 (1975), 595–604  mathnet  crossref  mathscinet  zmath
    8. I. M. Mikheev, “On lacunary series”, Math. USSR-Sb., 27:4 (1975), 481–502  mathnet  crossref  mathscinet  zmath
    9. I. M. Mikheev, “Lakunarnye podsistemy trigonometricheskoi sistemy funktsii”, UMN, 30:4(184) (1975), 255–256  mathnet  mathscinet  zmath
    10. E. V. Tokarev, “Subspaces of symmetric spaces of functions”, Funct. Anal. Appl., 13:2 (1979), 152–153  mathnet  crossref  mathscinet  zmath
    11. R. I. Ovsepian, “On the extraction, from general systems, of lacunary subsystems with the absolute convergence property”, Math. USSR-Sb., 39:4 (1981), 469–477  mathnet  crossref  mathscinet  zmath  isi
    12. Chen Gui-Jing, T.L Lai, C.Z Wei, “Convergence systems and strong consistency of least squares estimates in regression models”, Journal of Multivariate Analysis, 11:3 (1981), 319  crossref
    13. Tze Leung Lai, Ching Zong Wei, “Lacunary systems and generalized linear processes”, Stochastic Processes and their Applications, 14:2 (1983), 187  crossref
    14. S. Dhompongsa, “Almost sure invariance principles for the empirical process of lacunary sequences”, Acta Math Hungar, 49:1-2 (1987), 83  crossref  mathscinet  zmath  isi
    15. A. C. Offord, “Lacunary entire functions”, Math Proc Camb Phil Soc, 114:1 (1993), 67  crossref  mathscinet  zmath  isi
    16. S. Galstyan, R. I. Ovsepian, “Trigonometric series with rapidly decreasing coefficients”, Sb. Math., 187:11 (1996), 1577–1600  mathnet  crossref  crossref  mathscinet  zmath  isi
    17. S. V. Astashkin, “Identification of subsystems “majorized” by the Rademacher system”, Math. Notes, 65:4 (1999), 407–417  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. S. V. Astashkin, “On the selection of subsystems equivalent in distribution to the Rademacher system”, Math. Notes, 66:3 (1999), 384–388  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. S. V. Astashkin, “Systems of random variables equivalent in distribution to the Rademacher system and $\mathscr K$-closed representability of Banach couples”, Sb. Math., 191:6 (2000), 779–807  mathnet  crossref  crossref  mathscinet  zmath  isi
    20. A. I. Rubinshtein, “On best convergence”, Sb. Math., 192:2 (2001), 277–297  mathnet  crossref  crossref  mathscinet  zmath  isi
    21. E. M. Semenov, F. A. Sukochev, “The Banach–Saks index”, Sb. Math., 195:2 (2004), 263–285  mathnet  crossref  crossref  mathscinet  zmath  isi
    22. Guy Cohen, Michael Lin, “Extensions of the Menchoff-Rademacher theorem with applications to ergodic theory”, Isr J Math, 148:1 (2005), 41  crossref  mathscinet  zmath  isi  elib
    23. Cohen, G, “On random almost periodic series and random ergodic theory”, Ergodic Theory and Dynamical Systems, 26 (2006), 683  crossref  mathscinet  zmath  isi  elib
    24. Yu. Dabaghian, “Periodic orbit theory and the statistical analysis of scaling quantum graph spectra”, Phys Rev E, 75:5 (2007), 056214  crossref  mathscinet  adsnasa  isi
    25. Yu. A. Dabaghian, “Analytic description of statistics of spectra of quantum graphs”, Theoret. and Math. Phys., 156:1 (2008), 996–1019  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    26. S. V. Astashkin, “Independent functions in rearrangement invariant spaces and the Kruglov property”, Sb. Math., 199:7 (2008), 945–963  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    27. V. F. Gaposhkin, “On Independent and Stationary Subsystems of the Walsh System and Periodic Multiplicative Systems”, Math. Notes, 85:3 (2009), 340–347  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    28. S. V. Astashkin, “Rademacher functions in symmetric spaces”, Journal of Mathematical Sciences, 169:6 (2010), 725–886  mathnet  crossref  mathscinet  zmath  elib
    29. S. V. Astashkin, F. A. Sukochev, “Independent functions and the geometry of Banach spaces”, Russian Math. Surveys, 65:6 (2010), 1003–1081  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    30. Christoph Aistleitner, István Berkes, “On the central limit theorem for f (n k x)”, Probab. Theory Relat. Fields, 146:1-2 (2010), 267  crossref
    31. C. Aistleitner, “On the class of limits of lacunary trigonometric series”, Acta Math Hung, 129:1-2 (2010), 1  crossref
    32. S. V. Astashkin, R. S. Sukhanov, “On Certain Properties of Rademacher Chaos”, Math. Notes, 91:5 (2012), 613–624  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    33. Proc. Steklov Inst. Math., 276 (2012), 3–20  mathnet  crossref  mathscinet  isi  elib  elib
    34. István Berkes, Michel Weber, “On series Σc k f(kx) and Khinchin’s conjecture”, Isr. J. Math, 2014  crossref
    35. I. Berkes, R. Tichy, “On permutation-invariance of limit theorems”, Journal of Complexity, 2014  crossref
    36. M. Raseta, “On Lacunary Series with Random Gaps”, Acta Math. Hungar, 2014  crossref
    37. E. M. Semenov, S. N. Uksusov, “On superstrictly singular embeddings”, Dokl. Math, 89:3 (2014), 317  crossref
    38. Aistleitner Ch., Fukuyama K., “On the law of the iterated logarithm for trigonometric series with bounded gaps II”, J. Theor. Nr. Bordx., 28:2 (2016), 391–416  crossref  mathscinet  zmath  isi
    39. Fan A., “Almost everywhere convergence of ergodic series”, Ergod. Theory Dyn. Syst., 37:2 (2017), 490–511  crossref  mathscinet  zmath  isi  scopus
    40. A. I. Rubinshtein, “Ob odnom mnozhestve slabo multiplikativnykh sistem”, Matem. zametki, 105:3 (2019), 471–475  mathnet  crossref  elib
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