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Mat. Zametki, 2002, Volume 72, Issue 3, Pages 370–382 (Mi mz429)  

This article is cited in 12 scientific papers (total in 12 papers)

Approximation of Sobolev Classes by Their Finite-Dimensional Sections

V. N. Konovalov

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: We consider relative widths characterizing the best approximation of a fixed set by its sections of given dimension. For Sobolev classes of periodic functions of a single variable with constraints in $L_\infty$ or $L_1$ on higher-order derivatives, we present the exact orders of such widths in the spaces $L_q$.

DOI: https://doi.org/10.4213/mzm429

Full text: PDF file (234 kB)
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English version:
Mathematical Notes, 2002, 72:3, 337–349

Bibliographic databases:

UDC: 517.5
Received: 16.11.2001

Citation: V. N. Konovalov, “Approximation of Sobolev Classes by Their Finite-Dimensional Sections”, Mat. Zametki, 72:3 (2002), 370–382; Math. Notes, 72:3 (2002), 337–349

Citation in format AMSBIB
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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. Liu, YP, “Relative width of smooth classes of multivariate periodic functions with restrictions on iterated Laplace derivatives in the L-2-metric”, Acta Mathematica Scientia, 26:4 (2006), 720  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Liu, YP, “Relative average widths of Sobolev spaces in L-2(R-d)”, Analysis Mathematica, 34:1 (2008), 71  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Liu, YP, “Relative widths of smooth functions determined by fractional order derivatives”, Journal of Complexity, 24:2 (2008), 259  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Liu, YP, “THE RESEARCH PROGRESS OF BNU GROUP ON RELATIVE WIDTHS”, International Journal of Wavelets Multiresolution and Information Processing, 7:6 (2009), 803  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Xu, GQ, “The relative n-widths of Sobolev classes with restrictions”, Journal of Approximation Theory, 157:1 (2009), 19  crossref  mathscinet  isi  scopus  scopus
    6. Yang, LH, “Relative widths of smooth functions determined by linear differential operator”, Journal of Mathematical Analysis and Applications, 351:2 (2009), 734  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Yang W.ei, Liu Y.ongPing, “Relative n-widths of periodic convolution classes with NCVD-kernel and B-kernel”, Science China-Mathematics, 53:1 (2010), 165–172  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Xiao Weiwei, “Relative Infinite-Dimensional Width of Sobolev Classes W-P(R)(R)”, J. Math. Anal. Appl., 369:2 (2010), 575–582  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    9. Xiao W., “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  scopus
    10. Xu G. Zhang Zh., “Simultaneous Approximation of Sobolev Classes By Piecewise Cubic Hermite Interpolation”, Numer. Math.-Theory Methods Appl., 7:3 (2014), 317–333  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Yu. V. Malykhin, “Relative widths of Sobolev classes in the uniform and integral metrics”, Proc. Steklov Inst. Math., 293 (2016), 209–215  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    12. Y. Liu, G. Xu, J. Zhang, “Best restricted approximation of smooth function classes”, Tr. IMM UrO RAN, 24, no. 4, 2018, 283–294  mathnet  crossref  elib
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