Best Polynomial Approximations and Widths of Classes of Functions in the Space L 2

Best Polynomial Approximations and Widths of Classes of Functions in the Space L 2 ISSN 0001-4346, Mathematical Notes, 2018, Vol. 103, No. 2, pp. 308–312. © Pleiades Publishing, Ltd., 2018. Original Russian Text © S. B. Vakarchuk, 2018, published in Matematicheskie Zametki, 2018, Vol. 103, No. 2, pp. 307–311. SHORT COMMUNICATIONS Best Polynomial Approximations and Widths of Classes of Functions in the Space L S. B. Vakarchuk Alfred Nobel Dnepropetrovsk University, Dnepropetrovsk, Ukraine Received August 23, 2017 DOI: 10.1134/S0001434618010327 Keywords: best polynomial approximation, Fourier series, (ψ, β)-derivative, generalized modulus of continuity, n-width. 1. ON THE MODULI OF CONTINUITY IN L As a continuation of the studies of Shapiro and Boman [1], [2], the generalized moduli of continuity generated by arbitrary finite-difference operators with constant coefficients were considered in the papers of Babenko, Vasil’ev, Kozko, Rozhdestvenskii, Runovski, Ivanov and Kha Tkhi Min’ Khue, ´ Gorbachev, and others; see [3]–[12]). Let L be the space of Lebesgue measurable 2π-periodic functions f with finite norm 1/2 2π f := |f(x)| dx . Just as in [3], [4] we assign to f ∈ L the finite-difference operator Δ : L → L ,where h ∈ R; 2 2 2 M := {μ } is the collection of complex numbers satisfying the conditions j j∈Z 0 < |μ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Notes Springer Journals

Best Polynomial Approximations and Widths of Classes of Functions in the Space L 2

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Publisher
Pleiades Publishing
Copyright
Copyright © 2018 by Pleiades Publishing, Ltd.
Subject
Mathematics; Mathematics, general
ISSN
0001-4346
eISSN
1573-8876
D.O.I.
10.1134/S0001434618010327
Publisher site
See Article on Publisher Site

Abstract

ISSN 0001-4346, Mathematical Notes, 2018, Vol. 103, No. 2, pp. 308–312. © Pleiades Publishing, Ltd., 2018. Original Russian Text © S. B. Vakarchuk, 2018, published in Matematicheskie Zametki, 2018, Vol. 103, No. 2, pp. 307–311. SHORT COMMUNICATIONS Best Polynomial Approximations and Widths of Classes of Functions in the Space L S. B. Vakarchuk Alfred Nobel Dnepropetrovsk University, Dnepropetrovsk, Ukraine Received August 23, 2017 DOI: 10.1134/S0001434618010327 Keywords: best polynomial approximation, Fourier series, (ψ, β)-derivative, generalized modulus of continuity, n-width. 1. ON THE MODULI OF CONTINUITY IN L As a continuation of the studies of Shapiro and Boman [1], [2], the generalized moduli of continuity generated by arbitrary finite-difference operators with constant coefficients were considered in the papers of Babenko, Vasil’ev, Kozko, Rozhdestvenskii, Runovski, Ivanov and Kha Tkhi Min’ Khue, ´ Gorbachev, and others; see [3]–[12]). Let L be the space of Lebesgue measurable 2π-periodic functions f with finite norm 1/2 2π f := |f(x)| dx . Just as in [3], [4] we assign to f ∈ L the finite-difference operator Δ : L → L ,where h ∈ R; 2 2 2 M := {μ } is the collection of complex numbers satisfying the conditions j j∈Z 0 < |μ

Journal

Mathematical NotesSpringer Journals

Published: Mar 14, 2018

References

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