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Mat. Zametki, 1972, Volume 12, Issue 6, Pages 655–664 (Mi mz9930)  

This article is cited in 8 scientific papers (total in 9 papers)

A lower bound for the asymptotic characteristics of classes of functions with dominating mixed derivative

N. S. Bakhvalov

M. V. Lomonosov Moscow State University

Abstract: We obtain a new representation for classes of functions with dominating mixed derivative; using this representation we can obtain new lower bounds for the $\varepsilon$-entropy and for the errors in integration and interpolation for such classes.

Full text: PDF file (993 kB)

English version:
Mathematical Notes, 1972, 12:6, 833–838

Bibliographic databases:

UDC: 517.5
Received: 12.04.1972

Citation: N. S. Bakhvalov, “A lower bound for the asymptotic characteristics of classes of functions with dominating mixed derivative”, Mat. Zametki, 12:6 (1972), 655–664; Math. Notes, 12:6 (1972), 833–838

Citation in format AMSBIB
\Bibitem{Bak72}
\by N.~S.~Bakhvalov
\paper A lower bound for the asymptotic characteristics of classes of functions with dominating mixed derivative
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 6
\pages 655--664
\mathnet{http://mi.mathnet.ru/mz9930}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=333542}
\zmath{https://zbmath.org/?q=an:0249.41015}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 6
\pages 833--838
\crossref{https://doi.org/10.1007/BF01156040}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. E. Maiorov, “Multidimensional piecewise polynomial approximation on classes of functions with a dominant mixed derivative”, Math. USSR-Sb., 27:2 (1975), 269–288  mathnet  crossref  mathscinet  zmath
    2. V. E. Maiorov, “Various widths of the class $H_p^r$ in the space $L_q$”, Math. USSR-Izv., 13:1 (1979), 73–87  mathnet  crossref  mathscinet  zmath  isi
    3. V. V. Dubinin, “Cubature formulas for classes of functions with bounded mixed difference”, Russian Acad. Sci. Sb. Math., 76:2 (1993), 283–292  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. V. V. Dubinin, “Cubature formulae for Besov classes”, Izv. Math., 61:2 (1997), 259–283  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. N. Temirgaliev, “Efficiency of numerical integration algorithms related to divisor theory in cyclotomic fields”, Math. Notes, 61:2 (1997), 242–245  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. M. K. Kerimov, “Academician Nikolai Sergeevich Bakhvalov (on the occasion of his seventieth birthday)”, Comput. Math. Math. Phys., 45:4 (2005), 539–549  mathnet  mathscinet  zmath  elib
    7. S. P. Sidorov, “Optimal Recovery of Linear Functionals on Sets of Finite Dimension”, Math. Notes, 84:4 (2008), 561–567  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. N. Temirgaliev, S. S. Kudaibergenov, A. A. Shomanova, “An application of tensor products of functionals in problems of numerical integration”, Izv. Math., 73:2 (2009), 393–434  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. Romanyuk A.S., “Estimation of the Entropy Numbers and Kolmogorov Widths For the Nikol'Skii-Besov Classes of Periodic Functions of Many Variables”, Ukr. Math. J., 67:11 (2016), 1739–1757  crossref  mathscinet  isi  elib
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