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Izv. Akad. Nauk SSSR Ser. Mat., 1990, Volume 54, Issue 2, Pages 418–430 (Mi izv1101)  

This article is cited in 14 scientific papers (total in 14 papers)

Kolmogorov widths of classes of periodic functions of one and several variables

È. M. Galeev


Abstract: The order of Kolmogorov widths $d_N(\widetilde W_{\bar p}^{\bar\alpha},\widetilde L_q)$ are determined for the class $\widetilde W_{\bar p}^{\bar\alpha}=\bigcap\limits_{i=1}^m\widetilde W_{p^i}^{\alpha^i}$ that is the intersection of classes of periodic functions of one variable of “higher” smoothness, in the space $\widetilde L_q$ for $1<q<\infty$, and estimates from above for “low” smoothness, and also the order of Kolmogorov widths $d_N(\widetilde H_p^r,\widetilde L_q)$ is calculated for periodic functions of several variables in the space $\widetilde L_q$ for $1<p\leqslant q\leqslant 2$. The estimate from below for $d_N(\widetilde H_p^r,\widetilde L_q)$ reduces to the estimate from below of the width of a finite-dimensional set whose width is determined.

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English version:
Mathematics of the USSR-Izvestiya, 1991, 36:2, 435–448

Bibliographic databases:

UDC: 517.5
MSC: Primary 41A25, 41A46; Secondary 42B99
Received: 07.06.1988

Citation: È. M. Galeev, “Kolmogorov widths of classes of periodic functions of one and several variables”, Izv. Akad. Nauk SSSR Ser. Mat., 54:2 (1990), 418–430; Math. USSR-Izv., 36:2 (1991), 435–448

Citation in format AMSBIB
\Bibitem{Gal90}
\by \`E.~M.~Galeev
\paper Kolmogorov widths of classes of periodic functions of one and several variables
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1990
\vol 54
\issue 2
\pages 418--430
\mathnet{http://mi.mathnet.ru/izv1101}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1062521}
\zmath{https://zbmath.org/?q=an:0728.42002}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1991IzMat..36..435G}
\transl
\jour Math. USSR-Izv.
\yr 1991
\vol 36
\issue 2
\pages 435--448
\crossref{https://doi.org/10.1070/IM1991v036n02ABEH002029}


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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. D. Izaak, “Kolmogorov widths in finite-dimensional spaces with mixed norms”, Math. Notes, 55:1 (1994), 30–36  mathnet  crossref  mathscinet  zmath  isi  elib
    2. È. M. Galeev, “Kolmogorov $n$-width of some finite-dimensional sets in a mixed measure”, Math. Notes, 58:1 (1995), 774–778  mathnet  crossref  mathscinet  zmath  isi
    3. S. N. Kudryavtsev, “Diameters of classes of smooth functions”, Izv. Math., 59:4 (1995), 741–764  mathnet  crossref  mathscinet  zmath  isi
    4. È. M. Galeev, “Linear widths of Hölder–Nikol'skii classes of periodic functions of several variables”, Math. Notes, 59:2 (1996), 133–140  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. A. D. Izaak, “Widths of Hölder–Nikol'skij classes and finite-dimensional subsets in spaces with mixed norm”, Math. Notes, 59:3 (1996), 328–330  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. S. N. Kudryavtsev, “Bernstein width of a class of functions of finite smoothness”, Sb. Math., 190:4 (1999), 539–560  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. È. M. Galeev, “Widths of the Besov Classes $B_{p,\theta}^r(\mathbb T^d)$”, Math. Notes, 69:5 (2001), 605–613  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. S. N. Kudryavtsev, “Widths of classes of finitely smooth functions in Sobolev spaces”, Math. Notes, 77:4 (2005), 494–498  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. E. M. Galeev, “Poperechniki funktsionalnykh klassov i konechnomernykh mnozhestv”, Vladikavk. matem. zhurn., 13:2 (2011), 3–14  mathnet  elib
    10. Kudryavtsev S.N., “Generalized Haar series and their applications”, Anal Math, 37:2 (2011), 103–150  crossref  isi
    11. A.A. Vasil’eva, “Kolmogorov and linear widths of the weighted Besov classes with singularity at the origin”, Journal of Approximation Theory, 167 (2013), 1  crossref
    12. Yu. V. Malykhin, K. S. Ryutin, “The Product of Octahedra is Badly Approximated in the $\ell_{2,1}$-Metric”, Math. Notes, 101:1 (2017), 94–99  mathnet  crossref  crossref  mathscinet  isi  elib
    13. A. A. Vasileva, “Kolmogorovskie poperechniki klassov Soboleva na otrezke s ogranicheniyami na variatsiyu”, Tr. IMM UrO RAN, 25, no. 2, 2019, 48–66  mathnet  crossref  elib
    14. A. A. Vasileva, “Kolmogorovskie poperechniki peresechenii vesovykh klassov Soboleva na otrezke s ogranicheniyami na nulevuyu i pervuyu proizvodnye”, Izv. RAN. Ser. matem., 85:1 (2021), 3–26  mathnet  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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