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Matematicheskie Zametki, 2011, Volume 90, Issue 5, Pages 764–775
DOI: https://doi.org/10.4213/mzm8821 (Mi mzm8821) 		 
This article is cited in 32 scientific papers (total in 32 papers)

Best Polynomial Approximations in $L_2$ of Classes of $2\pi$-Periodic Functions and Exact Values of Their Widths

M. Sh. Shabozova, G. A. Yusupovb

a Institute of Mathematics, Academy of Sciences of Republic of Tajikistan
b Tajik National University, Dushanbe
Full-text PDF (503 kB) Citations (32)
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DOI: https://doi.org/10.4213/mzm8821
Abstract: We consider the problem of determining sharp inequalities between the best approximations of periodic differentiable functions by trigonometric polynomials and moduli of continuity of $m$th order in the space $L_2$ as well as present their applications. For some classes of functions defined by these moduli of continuity, we calculate the exact values of $n$-widths in $L_2$.
Keywords: best polynomial approximation, periodic differentiable function, trigonometric polynomial, modulus of continuity, the space $L_2$, $n$-width, Fourier series.
Received: 22.02.2010
Revised: 29.09.2010
English version:
Mathematical Notes, 2011, Volume 90, Issue 5, Pages 748–757
DOI: https://doi.org/10.1134/S0001434611110125
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: M. Sh. Shabozov, G. A. Yusupov, “Best Polynomial Approximations in $L_2$ of Classes of $2\pi$-Periodic Functions and Exact Values of Their Widths”, Mat. Zametki, 90:5 (2011), 764–775; Math. Notes, 90:5 (2011), 748–757
Citation in format AMSBIB
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\paper Best Polynomial Approximations in~$L_2$ of Classes of $2\pi$-Periodic Functions and Exact Values of Their Widths
\jour Mat. Zametki
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\issue 5
\pages 764--775
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    • This publication is cited in the following 32 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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