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

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.

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

Bibliographic databases:

UDC: 517.5

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
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
3. V. V. Dubinin, “Cubature formulas for classes of functions with bounded mixed difference”, Russian Acad. Sci. Sb. Math., 76:2 (1993), 283–292
4. V. V. Dubinin, “Cubature formulae for Besov classes”, Izv. Math., 61:2 (1997), 259–283
5. N. Temirgaliev, “Efficiency of numerical integration algorithms related to divisor theory in cyclotomic fields”, Math. Notes, 61:2 (1997), 242–245
6. M. K. Kerimov, “Academician Nikolai Sergeevich Bakhvalov (on the occasion of his seventieth birthday)”, Comput. Math. Math. Phys., 45:4 (2005), 539–549
7. S. P. Sidorov, “Optimal Recovery of Linear Functionals on Sets of Finite Dimension”, Math. Notes, 84:4 (2008), 561–567
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
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
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