Bounds for Fourier widths of classes of periodic functions with a mixed modulus of smoothness
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 78-94
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Order-exact bounds are obtained for Fourier widths of the Nikol'skii-Besov classes $\mathrm{SB}_{p\theta}^{\Omega,l} (\mathbb{T}^d)$ and Triebel-Lizorkin classes $\mathrm{SF}_{p\theta}^{\Omega,l} (\mathbb{T}^d)$ of functions with a given majorant $\Omega$ for the mixed modulus of smoothness of order $l$ in the space $L_q(\mathbb{T}^d)$ for all relations between the parameters $p$, $q$, and $\theta$ under some conditions on $\Omega$. The upper bounds follow from order-exact bounds for approximations of the classes $\mathrm{SB}_{p\theta}^{\Omega,l} (\mathbb{T}^d)$ and $\mathrm{SF}_{p\theta}^{\Omega,l} (\mathbb{T}^d)$ by special partial sums of Fourier series in the multiple system $\Psi_d$ of periodized Meyer wavelets.
Keywords:
fourier width, mixed modulus of smoothness, function spaces, wavelet system.
@article{TIMM_2015_21_4_a7,
author = {Sh. A. Balgimbaeva and T. I. Smirnov},
title = {Bounds for {Fourier} widths of classes of periodic functions with a mixed modulus of smoothness},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {78--94},
publisher = {mathdoc},
volume = {21},
number = {4},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a7/}
}
TY - JOUR AU - Sh. A. Balgimbaeva AU - T. I. Smirnov TI - Bounds for Fourier widths of classes of periodic functions with a mixed modulus of smoothness JO - Trudy Instituta matematiki i mehaniki PY - 2015 SP - 78 EP - 94 VL - 21 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a7/ LA - ru ID - TIMM_2015_21_4_a7 ER -
%0 Journal Article %A Sh. A. Balgimbaeva %A T. I. Smirnov %T Bounds for Fourier widths of classes of periodic functions with a mixed modulus of smoothness %J Trudy Instituta matematiki i mehaniki %D 2015 %P 78-94 %V 21 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a7/ %G ru %F TIMM_2015_21_4_a7
Sh. A. Balgimbaeva; T. I. Smirnov. Bounds for Fourier widths of classes of periodic functions with a mixed modulus of smoothness. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 78-94. http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a7/