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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 4, Pages 773–788 (Mi izv1845)  

This article is cited in 5 scientific papers (total in 5 papers)

Various widths of the class $H_p^r$ in the space $L_q$

V. E. Maiorov


Abstract: A method of reducing the computation of $n$-widths of compact sets of functions to the analogous problem for finite-dimensional compact sets is presented. Using this method the author obtains best possible (in the “power scale”) estimates for Kolmogorov, Aleksandrov and entropy $n$-widths of the class $H_p^r$ of functions $f(x)$, $x\in R^S$, that are $2\pi$-periodic in each variable, satisfy the inequality
$$ \|\frac{\partial^{rs}}{\partial x_1^r\cdots\partial x_s^r}\|_{L_p}\leqslant1 $$
and have the property that any Fourier coefficients with at least one zero index must be equal to zero.
Bibliography: 21 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1979, 13:1, 73–87

Bibliographic databases:

UDC: 517.5
MSC: Primary 41A46; Secondary 46E30
Received: 12.03.1976

Citation: V. E. Maiorov, “Various widths of the class $H_p^r$ in the space $L_q$”, Izv. Akad. Nauk SSSR Ser. Mat., 42:4 (1978), 773–788; Math. USSR-Izv., 13:1 (1979), 73–87

Citation in format AMSBIB
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\by V.~E.~Maiorov
\paper Various widths of the class $H_p^r$ in the space~$L_q$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 4
\pages 773--788
\mathnet{http://mi.mathnet.ru/izv1845}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=508826}
\zmath{https://zbmath.org/?q=an:0418.46020|0385.46012}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 1
\pages 73--87
\crossref{https://doi.org/10.1070/IM1979v013n01ABEH002012}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JB17800005}


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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. E. Maiorov, “On linear widths of Sobolev classes and chains of extremal subspaces”, Math. USSR-Sb., 41:3 (1982), 361–382  mathnet  crossref  mathscinet  zmath
    2. È. M. Galeev, “Some estimates for the diameters of the intersection of classes of functions”, Russian Math. Surveys, 37:4 (1982), 115–116  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Hermann König, “Spaces with large projection constants”, Isr J Math, 50:3 (1985), 181  crossref  mathscinet  zmath  isi
    4. V. N. Temlyakov, “Approximation of periodic functions of several variables by trigonometric polynomials, and widths of some classes of functions”, Math. USSR-Izv., 27:2 (1986), 285–322  mathnet  crossref  mathscinet  zmath
    5. Belinskii E., “the Approximation of Periodic-Functions of Several-Variables By Floating System of Exponents and the Trigonometric Widths”, 284, no. 6, 1985, 1294–1297  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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