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Uspekhi Mat. Nauk, 1973, Volume 28, Issue 2(170), Pages 65–119 (Mi umn4862)  

This article is cited in 18 scientific papers (total in 18 papers)

Some problems in the theory of simple and multiple trigonometric and orthogonal series

L. V. Zhizhiashvili


Abstract: In this article we give a brief account of the results on multiple trigonometric and orthogonal series that have been obtained so far and are fundamental from our point of view. We also state results on simple trigonometric and orthogonal series that are new or have been obtained recently.

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English version:
Russian Mathematical Surveys, 1973, 28:2, 65–127

Bibliographic databases:

UDC: 517.5
MSC: 42A50, 42A20, 42A24, 40A05
Received: 20.11.1972

Citation: L. V. Zhizhiashvili, “Some problems in the theory of simple and multiple trigonometric and orthogonal series”, Uspekhi Mat. Nauk, 28:2(170) (1973), 65–119; Russian Math. Surveys, 28:2 (1973), 65–127

Citation in format AMSBIB
\Bibitem{Zhi73}
\by L.~V.~Zhizhiashvili
\paper Some problems in the theory of simple and multiple trigonometric and orthogonal series
\jour Uspekhi Mat. Nauk
\yr 1973
\vol 28
\issue 2(170)
\pages 65--119
\mathnet{http://mi.mathnet.ru/umn4862}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=404984}
\zmath{https://zbmath.org/?q=an:0259.42027|0273.42018}
\transl
\jour Russian Math. Surveys
\yr 1973
\vol 28
\issue 2
\pages 65--127
\crossref{https://doi.org/10.1070/RM1973v028n02ABEH001536}


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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. L. V. Zhizhiashvili, “On trigonometric Fourier series”, Math. USSR-Sb., 29:4 (1976), 521–546  mathnet  crossref  mathscinet  zmath  isi
    2. Sh. A. Alimov, V. A. Il'in, E. M. Nikishin, “Convergence problems of multiple trigonometric series and spectral decompositions. I”, Russian Math. Surveys, 31:6 (1976), 29–86  mathnet  crossref  mathscinet  zmath
    3. T. I. Akhobadze, “Functions of bounded generalized second variation”, Math. USSR-Sb., 37:2 (1980), 261–294  mathnet  crossref  mathscinet  zmath  isi
    4. L. D. Gogoladze, “On the existence of conjugate functions of several variables”, Math. USSR-Sb., 53:2 (1986), 481–488  mathnet  crossref  mathscinet  zmath
    5. A. A. Talalyan, “On uniqueness of multiple trigonometric series”, Math. USSR-Sb., 60:1 (1988), 107–131  mathnet  crossref  mathscinet  zmath
    6. A. A. Talalyan, “On some uniqueness properties of multiple trigonometric series and harmonic functions”, Math. USSR-Izv., 32:3 (1989), 627–654  mathnet  crossref  mathscinet  zmath
    7. 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
    8. J.F Price, I.H Sloan, “Pointwise convergence of multiple Fourier series: Sufficient conditions and an application to numerical integration”, Journal of Mathematical Analysis and Applications, 169:1 (1992), 140  crossref
    9. M. G. Grigoryan, “On some properties of orthogonal systems”, Russian Acad. Sci. Izv. Math., 43:2 (1994), 261–289  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. A. M. Stokolos, “On the strong differentiation of integrals of functions from Hölder classes”, Math. Notes, 55:1 (1994), 57–70  mathnet  crossref  mathscinet  zmath  isi
    11. M. I. Dyachenko, “$u$-convergence of multiple Fourier series”, Izv. Math., 59:2 (1995), 353–366  mathnet  crossref  mathscinet  zmath  isi
    12. M. I. Dyachenko, “Uniform convergence of double Fourier series for classes of functions with anisotropic smoothness”, Math. Notes, 59:6 (1996), 680–686  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. M. M. Lekishvili, A. N. Danelia, “Multidimensional conjugation operators and deformations of the classes $Z(\omega^{(2)};C(T^m))$”, Math. Notes, 63:6 (1998), 752–759  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. V. A. Okulov, “Some structure properties of conjugate functions in $L(T^N)$”, Sb. Math., 189:5 (1998), 727–756  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. A. N. Bakhvalov, “$\lambda$-Divergence of the Fourier Series of Continuous Functions of Several Variables”, Math. Notes, 72:4 (2002), 454–465  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. M. G. Grigoryan, “On the $L^p_\mu$-strong property of orthonormal systems”, Sb. Math., 194:10 (2003), 1503–1532  mathnet  crossref  crossref  mathscinet  zmath  isi
    17. M. G. Plotnikov, “Coefficients of convergent multiple Walsh-Paley series”, Sb. Math., 203:9 (2012), 1295–1309  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    18. D. G. Dzhumabaeva, M. I. Dyachenko, E. D. Nursultanov, “On convergence of multiple trigonometric series with monotone coefficients”, Siberian Math. J., 58:2 (2017), 205–214  mathnet  crossref  crossref  isi  elib  elib
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