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Mathematics of the USSR-Izvestiya, 1979, Volume 13, Issue 1, Pages 73–87
DOI: https://doi.org/10.1070/IM1979v013n01ABEH002012
(Mi im1845)
 

This article is cited in 6 scientific papers (total in 6 papers)

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

V. E. Maiorov
References:
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
$$ \biggl\|\frac{\partial^{rs}}{\partial x_1^r\cdots\partial x_s^r}\biggr\|_{L_p}\leqslant1 $$
and have the property that any Fourier coefficients with at least one zero index must be equal to zero.
Bibliography: 21 titles.
Received: 12.03.1976
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1978, Volume 42, Issue 4, Pages 773–788
Bibliographic databases:
UDC: 517.5
MSC: Primary 41A46; Secondary 46E30
Language: English
Original paper language: Russian
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
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\mathscinet{http://mathscinet.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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1979JB17800005}
Linking options:
  • https://www.mathnet.ru/eng/im1845
  • https://doi.org/10.1070/IM1979v013n01ABEH002012
  • https://www.mathnet.ru/eng/im/v42/i4/p773
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:399
    Russian version PDF:124
    English version PDF:13
    References:93
    First page:1
     
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