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Uspekhi Mat. Nauk, 1964, Volume 19, Issue 1(115), Pages 3–69 (Mi umn6161)  

This article is cited in 40 scientific papers (total in 41 papers)

Solved and unsolved problems in the theory of trigonometric and orthogonal series

P. L. Ul'yanov


Full text: PDF file (6546 kB)

English version:
Russian Mathematical Surveys, 1964, 19:1, 1–62

Bibliographic databases:

UDC: 517.512.2/4+517.512.7
MSC: 42A20, 42A16, 42A24, 42C20
Received: 11.05.1963

Citation: P. L. Ul'yanov, “Solved and unsolved problems in the theory of trigonometric and orthogonal series”, Uspekhi Mat. Nauk, 19:1(115) (1964), 3–69; Russian Math. Surveys, 19:1 (1964), 1–62

Citation in format AMSBIB
\Bibitem{Uly64}
\by P.~L.~Ul'yanov
\paper Solved and unsolved problems in the theory of trigonometric and orthogonal series
\jour Uspekhi Mat. Nauk
\yr 1964
\vol 19
\issue 1(115)
\pages 3--69
\mathnet{http://mi.mathnet.ru/umn6161}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=161085}
\zmath{https://zbmath.org/?q=an:0125.31208}
\transl
\jour Russian Math. Surveys
\yr 1964
\vol 19
\issue 1
\pages 1--62
\crossref{https://doi.org/10.1070/RM1964v019n01ABEH004136}


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    Citing articles on Google Scholar: Russian citations, English citations
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    2. Niranjan Singh, “On the absolute Cesaro summability factors of trigonometric series”, Proc Edin Math Soc, 16:1 (1968), 71  crossref  mathscinet
    3. È. A. Storozhenko, “On the order of approximation by Fejér sums”, Math. USSR-Izv., 3:1 (1978), 37–49  mathnet  crossref  mathscinet  zmath
    4. Prem Chandra, “Absolute Cesàro summability factors of trigonometric series”, Rend Circ Mat Palermo, 21:1-2 (1972), 140  crossref  mathscinet  zmath
    5. P. L. Ul'yanov, “Representation of functions by series and classes $\varphi(L)$”, Russian Math. Surveys, 27:2 (1972), 1–54  mathnet  crossref  mathscinet  zmath
    6. Z. A. Chanturiya, “Bases of the space of continuous functions”, Math. USSR-Sb., 17:4 (1972), 583–602  mathnet  crossref  mathscinet  zmath
    7. A. M. Olevskii, “An example of an orthonormal system of convergence in $C$ but not in $L^2$”, Math. USSR-Sb., 20:1 (1973), 145–153  mathnet  crossref  mathscinet  zmath
    8. S. V. Bochkarev, “On a problem of Zygmund”, Math. USSR-Izv., 7:3 (1973), 629–637  mathnet  crossref  mathscinet  zmath
    9. 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
    10. A. S. Krantsberg, “On divergent Fourier series in orthogonal systems”, Math. USSR-Sb., 22:4 (1974), 547–560  mathnet  crossref  mathscinet  zmath
    11. S. V. Bochkarev, “On the absolute convergence of Fourier series in bounded complete orthonormal systems of functions”, Math. USSR-Sb., 22:1 (1974), 201–216  mathnet  crossref  mathscinet  zmath
    12. V. A. Skvortsov, “Example of a Walsh series with a subsequence of partial sums converging everywhere to zero”, Math. USSR-Sb., 26:4 (1975), 471–491  mathnet  crossref  mathscinet  zmath
    13. B. S. Kashin, “On a complete orthonormal system”, Math. USSR-Sb., 28:3 (1976), 315–324  mathnet  crossref  mathscinet  zmath  isi
    14. S. N. Poleshchuk, “On exact Weyl multipliers”, Math. USSR-Sb., 36:1 (1980), 101–110  mathnet  crossref  mathscinet  zmath  isi
    15. P. L. Ul'yanov, “On Fourier coefficients”, Math. USSR-Sb., 38:1 (1981), 11–29  mathnet  crossref  mathscinet  zmath  isi
    16. I. N. Pak, “On the sums of trigonometric series”, Russian Math. Surveys, 35:2 (1980), 105–168  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. N. B. Pogosyan, “Summability to $+\infty $ of Haar and Walsh series”, Russian Math. Surveys, 35:2 (1980), 255–256  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    18. K. S. Kazarian, “On some questions in the theory of orthogonal series”, Math. USSR-Sb., 47:1 (1984), 269–285  mathnet  crossref  mathscinet  zmath
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    23. P. L. Ul'yanov, “Luzin's work on the metric theory of functions”, Russian Math. Surveys, 40:3 (1985), 15–77  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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    25. Al. A. Privalov, “On an orthogonal trigonometric basis”, Math. USSR-Sb., 72:2 (1992), 363–372  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    26. 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
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    28. M. I. Dyachenko, “Some problems in the theory of multiple trigonometric series”, Russian Math. Surveys, 47:5 (1992), 103–171  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    29. Kozlov A., “Multifunctionality and Interchangeability in Operations of the Thoracic Legs of the Gaddisworms Phryganea-Grandis (Insecta, Trichoptera)”, Zool. Zhurnal, 71:11 (1992), 61–66  isi
    30. Sh. T. Tetunashvili, “Trigonometric, Walsh, and Haar null-series”, Sb. Math., 187:3 (1996), 413–450  mathnet  crossref  crossref  mathscinet  zmath  isi
    31. G. G. Gevorkyan, K. A. Navasardyan, “On Walsh series with monotone coefficients”, Izv. Math., 63:1 (1999), 37–55  mathnet  crossref  crossref  mathscinet  zmath  isi
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    34. S. V. Konyagin, “On Uniformly Convergent Rearrangements of Trigonometric Fourier Series”, Journal of Mathematical Sciences, 155:1 (2008), 81–88  mathnet  crossref  mathscinet  zmath  elib
    35. S. I. Dudov, A. M. Zakharov, D. V. Prokhorov, A. P. Khromov, “Petr Lavrentevich Ulyanov”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 7:1 (2007), 89–93  mathnet  elib
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