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

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

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
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
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
4. Xiao Weiwei, “Relative infinite-dimensional width of Sobolev classes $W^r_p(\mathbb R)$”, J. Math. Anal. Appl., 369:2 (2010), 575–582
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
6. “Yurii Nikolaevich Subbotin. (K semidesyatipyatiletiyu so dnya rozhdeniya)”, Tr. IMM UrO RAN, 17, no. 3, 2011, 8–13
7. Yu. N. Subbotin, S. A. Telyakovskii, “Ob otnositelnykh poperechnikakh klassov differentsiruemykh funktsii. III”, Tr. IMM UrO RAN, 17, no. 3, 2011, 300–302
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