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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 4, Pages 81–104 (Mi izv32)  

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

Diameters of classes of smooth functions

S. N. Kudryavtsev

Institute for High-Performance Computer Systems, Russian Academy of Sciences

Abstract: We describe the weak asymptotic behaviour of diameters of $n$-th order of the unit ball of $W_p^l H^\omega (I^d)$ in $L_q(I^d)$, where $I=(0,1)$, in dependence on $n$. Namely we consider the Kolmogorov diameter, the Gel'fand diameter, the linear diameter, the Aleksandrov diameter and the entropy diameter.

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English version:
Izvestiya: Mathematics, 1995, 59:4, 741–764

Bibliographic databases:

MSC: 41A46
Received: 29.03.1993

Citation: S. N. Kudryavtsev, “Diameters of classes of smooth functions”, Izv. RAN. Ser. Mat., 59:4 (1995), 81–104; Izv. Math., 59:4 (1995), 741–764

Citation in format AMSBIB
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\by S.~N.~Kudryavtsev
\paper Diameters of classes of smooth functions
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 4
\pages 81--104
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\zmath{https://zbmath.org/?q=an:0865.41030}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 4
\pages 741--764
\crossref{https://doi.org/10.1070/IM1995v059n04ABEH000032}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000169556400005}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. S. N. Kudryavtsev, “Approximation of the derivatives of finitely smooth functions belonging to non-isotropic classes”, Izv. Math., 68:1 (2004), 77–123  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. 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
    4. V. S. Romanyuk, “Nonlinear Diameters of Classes of Smooth Functions Defined on the Unit Sphere in $\mathbb R^{d}$”, Math. Notes, 85:1 (2009), 136–141  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Kudryavtsev S.N., “Generalized Haar series and their applications”, Anal Math, 37:2 (2011), 103–150  crossref  isi
    6. Li Yu.W. Fang G.S., “Bernstein N-Widths of Besov Embeddings on Lipschitz Domains”, Acta. Math. Sin.-English Ser., 29:12 (2013), 2283–2294  crossref  isi
    7. S. N. Kudryavtsev, “Extension of functions in non-isotropic Nikolskii–Besov spaces and approximation of their derivatives”, Izv. Math., 82:5 (2018), 931–983  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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