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Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 4, Pages 53–63 (Mi timm1353)  

One-sided integral approximations of the generalized Poisson kernel by trigonometric polynomials

A. G. Babenkoa, T. Z. Naumab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg

Abstract: We consider the generalized Poisson kernel $\Pi_{q,\alpha}=\cos(\alpha \pi/2)P +\sin(\alpha\pi/2)Q$ with $q\in(-1,1)$ and $\alpha\in\mathbb{R}$, which is a linear combination of the Poisson kernel $P(t)=1/2+\sum_{k=1}^\infty q^k\cos{kt}$ and the conjugate Poisson kernel $Q(t)=\sum\nolimits_{k=1}^\infty q^k\sin kt$. The values of the best upper and lower integral approximations of the kernel $\Pi_{q,\alpha}$ by trigonometric polynomials of order not exceeding a given number are found. The corresponding polynomials of the best one-sided approximation are obtained.

Keywords: constrained approximation, trigonometric polynomials, generalized Poisson kernel.

Funding Agency Grant Number
Russian Science Foundation 14-11-00702


DOI: https://doi.org/10.21538/0134-4889-2016-22-4-53-63

Full text: PDF file (223 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2018, 300, suppl. 1, 38–48

Bibliographic databases:

UDC: 517.518.834
MSC: 42A10, 41A29
Received: 26.09.2016

Citation: A. G. Babenko, T. Z. Naum, “One-sided integral approximations of the generalized Poisson kernel by trigonometric polynomials”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 4, 2016, 53–63; Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 38–48

Citation in format AMSBIB
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