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Izv. Akad. Nauk SSSR Ser. Mat., 1974, Volume 38, Issue 6, Pages 1393–1407 (Mi izv2018)  

This article is cited in 9 scientific papers (total in 9 papers)

An estimate of the rate of approximation of a continuous function and its conjugate by Fourier sums on a set of total measure

K. I. Oskolkov


Abstract: In this paper, estimates of the rate of convergence almost everywhere of the Fourier series of a continuous function and its conjugate are obtained. These estimates, expressed in terms of its best approximation functions and its modulus of continuity, cannot be strengthened in a number of cases.

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English version:
Mathematics of the USSR-Izvestiya, 1974, 8:6, 1372–1386

Bibliographic databases:

UDC: 517.512
MSC: Primary 41A25, 42A08, 42A20; Secondary 41A50
Received: 22.06.1973

Citation: K. I. Oskolkov, “An estimate of the rate of approximation of a continuous function and its conjugate by Fourier sums on a set of total measure”, Izv. Akad. Nauk SSSR Ser. Mat., 38:6 (1974), 1393–1407; Math. USSR-Izv., 8:6 (1974), 1372–1386

Citation in format AMSBIB
\Bibitem{Osk74}
\by K.~I.~Oskolkov
\paper An estimate of the rate of approximation of a~continuous function and its conjugate by Fourier sums on a~set of total measure
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1974
\vol 38
\issue 6
\pages 1393--1407
\mathnet{http://mi.mathnet.ru/izv2018}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=358198}
\zmath{https://zbmath.org/?q=an:0307.42002}
\transl
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 6
\pages 1372--1386
\crossref{https://doi.org/10.1070/IM1974v008n06ABEH002152}


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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. K. I. Oskolkov, “Approximation properties of summable functions on sets of full measure”, Math. USSR-Sb., 32:4 (1977), 489–514  mathnet  crossref  mathscinet  zmath  isi
    2. V. M. Badkov, “Approximation properties of Fourier series in orthogonal polynomials”, Russian Math. Surveys, 33:4 (1978), 53–117  mathnet  crossref  mathscinet  zmath
    3. 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
    4. N Kirchhoff, R.J Nessel, “Divergence almost everywhere of a pointwise comparison of trigonometric convolution processes with their discrete analogues”, Journal of Approximation Theory, 70:1 (1992), 29  crossref
    5. A. N. Bakhvalov, “Divergence everywhere of the Fourier series of continuous functions of several variables”, Sb. Math., 188:8 (1997), 1153–1170  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. 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
    7. I. L. Bloshanskii, T. A. Matseevich, “A Weak Generalize Localization of Multiple Fourier Series of Continuous Functions with a Certain Module of Continuity”, Journal of Mathematical Sciences, 155:1 (2008), 31–46  mathnet  crossref  mathscinet  zmath
    8. St. Petersburg Math. J., 26:5 (2015), 741–756  mathnet  crossref  mathscinet  isi  elib  elib
    9. D. A. Grafov, “Equiconvergence of expansions into triple trigonometric series and Fourier integral for continuous functions with a certain modulus of continuity”, Moscow University Mathematics Bulletin, 70:1 (2015), 24–32  mathnet  crossref  mathscinet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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