Widths of Classes of Periodic Differentiable Functions in the Space~$L_{2}[0,2\pi]$
Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 616-623
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We obtain exact values of different $n$-widths for classes of differentiable periodic functions in the space $L_{2}[0,2\pi]$ satisfying the constraint
$$
\biggl(\int_{0}^{h}\omega_{m}^{p}(f^{(r)};t)\,dt\biggr)^{1/p}\le\Phi(h),
$$
where $0$, $1/r$, $r\in\mathbb{N}$, and $\omega_{m}(f^{(r)};t)$ is the modulus of continuity of $m$th order of the derivative $f^{(r)}(x)\in L_{2}[0,2\pi]$.
Keywords:
differentiable periodic function, width in the sense of Bernstein, Kolmogorov, Gelfand, the space $L_{2}[0,2\pi]$, trigonometric polynomial, Fourier series, modulus of continuity, linear operator.
@article{MZM_2010_87_4_a12,
author = {M. Sh. Shabozov},
title = {Widths of {Classes} of {Periodic} {Differentiable} {Functions} in the {Space~}$L_{2}[0,2\pi]$},
journal = {Matemati\v{c}eskie zametki},
pages = {616--623},
publisher = {mathdoc},
volume = {87},
number = {4},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a12/}
}
M. Sh. Shabozov. Widths of Classes of Periodic Differentiable Functions in the Space~$L_{2}[0,2\pi]$. Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 616-623. http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a12/