One-sided integral approximations of the generalized Poisson kernel by trigonometric polynomials
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 53-63
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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.
@article{TIMM_2016_22_4_a5,
author = {A. G. Babenko and T. Z. Naum},
title = {One-sided integral approximations of the generalized {Poisson} kernel by trigonometric polynomials},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {53--63},
publisher = {mathdoc},
volume = {22},
number = {4},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a5/}
}
TY - JOUR AU - A. G. Babenko AU - T. Z. Naum TI - One-sided integral approximations of the generalized Poisson kernel by trigonometric polynomials JO - Trudy Instituta matematiki i mehaniki PY - 2016 SP - 53 EP - 63 VL - 22 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a5/ LA - ru ID - TIMM_2016_22_4_a5 ER -
%0 Journal Article %A A. G. Babenko %A T. Z. Naum %T One-sided integral approximations of the generalized Poisson kernel by trigonometric polynomials %J Trudy Instituta matematiki i mehaniki %D 2016 %P 53-63 %V 22 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a5/ %G ru %F TIMM_2016_22_4_a5
A. G. Babenko; T. Z. Naum. One-sided integral approximations of the generalized Poisson kernel by trigonometric polynomials. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 53-63. http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a5/