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Izv. Vyssh. Uchebn. Zaved. Mat., 2015, Number 11, Pages 3–22 (Mi ivm9048)  

This article is cited in 4 scientific papers (total in 4 papers)

Inequalities of Kolmogorov's type for derived functions in two variables and application to approximation by an “angle”

S. B. Vakarchuka, A. V. Shvachkob

a Chair of Economic Cybernetics and Mathematical Methods in Economy, Alfred Nobel University of Dnepropetrovsk, 18 Naberezhnaya Lenina str., Dnepropetrovsk, 49000 Unkraine
b Chair of Higher Mathematics, Dnepropetrovsk State Agrarian-Economic University, 25 Voroshilov str., Dnepropetrovsk, 49600 Ukraine

Abstract: For functions of two variables we obtain sharp inequalities of Kolmogorov's type for partial and mixed intermediate derivatives. We also consider applications of the results to some problems of approximation of functions of two variables by angles and obtain a series of relations which are exact in definite sense.

Keywords: Hermite polynomials, Fourier–Hermite series, inequalities of Kolmogorov's type, the best approximation by angle, generalized polynomial.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:11, 1–18

UDC: 517.5
Received: 14.03.2014

Citation: S. B. Vakarchuk, A. V. Shvachko, “Inequalities of Kolmogorov's type for derived functions in two variables and application to approximation by an “angle””, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 11, 3–22; Russian Math. (Iz. VUZ), 59:11 (2015), 1–18

Citation in format AMSBIB
\Bibitem{VakShv15}
\by S.~B.~Vakarchuk, A.~V.~Shvachko
\paper Inequalities of Kolmogorov's type for derived functions in two variables and application to approximation by an ``angle''
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 11
\pages 3--22
\mathnet{http://mi.mathnet.ru/ivm9048}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 11
\pages 1--18
\crossref{https://doi.org/10.3103/S1066369X15110018}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84945207665}


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    This publication is cited in the following articles:
    1. S. V. Konyagin, A. A. Kuleshov, V. E. Maiorov, “Some problems in the theory of ridge functions”, Proc. Steklov Inst. Math., 301 (2018), 144–169  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. S. B. Vakarchuk, “O priblizhenii klassicheskimi ortogonalnymi polinomami s vesom v prostranstvakh $L_{2,\gamma}(a,b)$ i o poperechnikakh funktsionalnykh klassov”, Izv. vuzov. Matem., 2019, no. 12, 37–51  mathnet  crossref
    3. M. Sh. Shabozov, M. O. Akobirshoev, “O neravenstvakh tipa Kolmogorova dlya periodicheskikh funktsii dvukh peremennykh v $L_2$”, Chebyshevskii sb., 20:2 (2019), 348–365  mathnet  crossref
    4. Shabozov M.Sh. Dzhurakhonov O.A., “Upper Bounds For the Approximation of Some Classes of Bivariate Functions By Triangular Fourier-Hermite Sums in the Space l-2,l-Rho(Double-Struck Capital R-2)”, Anal. Math., 45:4 (2019), 823–840  crossref  isi
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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