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Izv. Vyssh. Uchebn. Zaved. Mat., 2019, Number 12, Pages 37–51 (Mi ivm9525)  

This article is cited in 1 scientific paper (total in 1 paper)

Approximation by classical orthogonal polynomials with weight in spaces $L_{2,\gamma}(a,b)$ and widths of some functional classes

S. B. Vakarchuk

Alfred Nobel University, 18 Sicheslavska Seafront, Dnipro, 49000 Ukraine

Abstract: Questions of the approximation of functions from classes $W^r_2(D_{\gamma};(a,b))$, $r=2,3,\ldots,$ by classical orthogonal polynomials have been analyzed in the spaces $L_{2,\gamma}(a,b)$ with a weight $\gamma$. For different widths estimates above and below were obtained on the classes $W^r_2(\Omega_{m,\gamma}, \Psi; (a,b))$, where $r\in \mathbb{Z}_{+}$, $m \in \mathbb{N}$, $\Psi$ is a majorant, $\Omega_{m,\gamma}$ is a generalized modulus of continuity of $m$-th order. The condition on majorant has been indicated when we can to compute the exact values of widths if it be fulfilled. Some concrete examples of the obtained exact results are reduced. Estimates (including exact) of the supremums of Fourier coefficients were obtained on the all indicated classes.

Keywords: classical orthogonal polynom, orthonormal polynomial system, best polynomial approximation, width, generalized modulus of continuity, majorant, Fourier coefficient.

DOI: https://doi.org/10.26907/0021-3446-2019-12-37-51

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:12, 32–44

Bibliographic databases:

UDC: 517.518
Received: 28.12.2018
Revised: 24.02.2019
Accepted: 27.03.2019

Citation: S. B. Vakarchuk, “Approximation by classical orthogonal polynomials with weight in spaces $L_{2,\gamma}(a,b)$ and widths of some functional classes”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 12, 37–51; Russian Math. (Iz. VUZ), 63:12 (2019), 32–44

Citation in format AMSBIB
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\by S.~B.~Vakarchuk
\paper Approximation by classical orthogonal polynomials with weight in spaces $L_{2,\gamma}(a,b)$ and widths of some functional classes
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2019
\issue 12
\pages 37--51
\mathnet{http://mi.mathnet.ru/ivm9525}
\crossref{https://doi.org/10.26907/0021-3446-2019-12-37-51}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2019
\vol 63
\issue 12
\pages 32--44
\crossref{https://doi.org/10.3103/S1066369X19120041}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85078351633}


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    This publication is cited in the following articles:
    1. S. B. Vakarchuk, “Estimates of the Values of $n$-Widths of Classes of Analytic Functions in the Weight Spaces $H_{2,\gamma}(D)$”, Math. Notes, 108:6 (2020), 775–790  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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