This article is cited in 33 papers

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

M. Sh. Shabozov^a, G. A. Yusupov<sup>b

a</sup> Institute of Mathematics, Academy of Sciences of Republic of Tajikistan
^b Tajik National University, Dushanbe

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.

UDC: 517.5

Received: 22.02.2010
Revised: 29.09.2010

DOI: 10.4213/mzm8821

 English version: Mathematical Notes, 2011, 90:5, 748–757

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