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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2008, Volume 14, Number 3, Pages 19–37
(Mi timm37)
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This article is cited in 12 scientific papers (total in 12 papers)
Integral approximation of the characteristic function of an interval by trigonometric polynomials
A. G. Babenkoa, Yu. V. Kryakinb a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Mathematical Institute University of Wroclaw
Abstract:
We prove that the value $E_{n-1}(\chi_h)_L$ of the best integral approximation of the characteristic function $\chi_h$ of an interval $(-h,h)$ on the period $[-\pi,\pi)$ by trigonometric polynomials of degree at most $n-1$ is expressed in terms of zeros of the Bernstein function $\cos\{[nt-\arccos2q-(1+q^2)\cos t]/(1+q^2-2q\cos t)\}$, $t\in[0,\pi]$, $q\in(-1,1)$. Here, the parameters $q$, $h$, and $n$ are connected in a special way; in particular, $q=\sec h-\operatorname{tg} h$ при $h=\pi/n$.
Received: 03.05.2008
Citation:
A. G. Babenko, Yu. V. Kryakin, “Integral approximation of the characteristic function of an interval by trigonometric polynomials”, Trudy Inst. Mat. i Mekh. UrO RAN, 14, no. 3, 2008, 19–37; Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S19–S38
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Abstract page: | 672 | Full-text PDF : | 181 | References: | 44 |
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