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Trudy Mat. Inst. Steklova, 2005, Volume 248, Pages 250–261 (Mi tm135)  

This article is cited in 6 scientific papers (total in 7 papers)

On Relative Widths of Classes of Differentiable Functions

Yu. N. Subbotina, S. A. Telyakovskiib

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The Kolmogorov widths $d_{2n} (W^r_C, C)$ and relative widths $K_{2n}(W^r_C,MW^j_C,C)$ of the class $W^r_C$ with respect to $MW^j_C$, where $j < r$, are considered. The minimal multiplier $M$ for which these widths are equal is estimated from above and below; the bounds obtained show that this minimal value is asymptotically equal to the Favard constant $\mathcal K_{r-j}$ as $n \to \infty $.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2005, 248, 243–254

Bibliographic databases:
UDC: 517.224
Received in September 2004

Citation: Yu. N. Subbotin, S. A. Telyakovskii, “On Relative Widths of Classes of Differentiable Functions”, Studies on function theory and differential equations, Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 248, Nauka, MAIK Nauka/Inteperiodika, M., 2005, 250–261; Proc. Steklov Inst. Math., 248 (2005), 243–254

Citation in format AMSBIB
\Bibitem{SubTel05}
\by Yu.~N.~Subbotin, S.~A.~Telyakovskii
\paper On Relative Widths of Classes of Differentiable Functions
\inbook Studies on function theory and differential equations
\bookinfo Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2005
\vol 248
\pages 250--261
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm135}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2165932}
\zmath{https://zbmath.org/?q=an:1121.41027}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 248
\pages 243--254


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    This publication is cited in the following articles:
    1. Liu Yongping, Xiao Weiwei, “Relative average widths of Sobolev spaces in $L_2(\mathbb R^d)$”, Anal. Math., 34:1 (2008), 71–82  crossref  mathscinet  zmath  isi  elib  scopus
    2. Yu. N. Subbotin, S. A. Telyakovskii, “On the Equality of Kolmogorov and Relative Widths of Classes of Differentiable Functions”, Math. Notes, 86:3 (2009), 432–439  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Yu. N. Subbotin, S. A. Telyakovskii, “Sharpening of the estimates for relative widths of classes of differentiable functions”, Proc. Steklov Inst. Math., 269 (2010), 235–246  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    4. Xiao Weiwei, “Relative infinite-dimensional width of Sobolev classes $W^r_p(\mathbb R)$”, J. Math. Anal. Appl., 369:2 (2010), 575–582  crossref  mathscinet  zmath  isi  elib  scopus
    5. Xiao Weiwei, “Relative widths of function classes of $L_2(T)$ defined by a linear differential operator in $L_q(T)$”, Anal. Math., 37:1 (2011), 65–81  crossref  mathscinet  zmath  isi  elib  scopus
    6. “Yurii Nikolaevich Subbotin. (K semidesyatipyatiletiyu so dnya rozhdeniya)”, Tr. IMM UrO RAN, 17, no. 3, 2011, 8–13  mathnet
    7. Yu. N. Subbotin, S. A. Telyakovskii, “Ob otnositelnykh poperechnikakh klassov differentsiruemykh funktsii. III”, Tr. IMM UrO RAN, 17, no. 3, 2011, 300–302  mathnet  elib
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