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This article is cited in 6 scientific papers (total in 6 papers)
Various widths of the class $H_p^r$ in the space $L_q$
V. E. Maiorov
Abstract:
A method of reducing the computation of $n$-widths of compact sets of functions to the analogous problem for finite-dimensional compact sets is presented. Using this method the author obtains best possible (in the “power scale”) estimates for Kolmogorov, Aleksandrov and entropy $n$-widths of the class $H_p^r$ of functions $f(x)$, $x\in R^S$, that are
$2\pi$-periodic in each variable, satisfy the inequality
$$
\biggl\|\frac{\partial^{rs}}{\partial x_1^r\cdots\partial x_s^r}\biggr\|_{L_p}\leqslant1
$$
and have the property that any Fourier coefficients with at least one zero index must be equal to zero.
Bibliography: 21 titles.
Received: 12.03.1976
Citation:
V. E. Maiorov, “Various widths of the class $H_p^r$ in the space $L_q$”, Izv. Akad. Nauk SSSR Ser. Mat., 42:4 (1978), 773–788; Math. USSR-Izv., 13:1 (1979), 73–87
Linking options:
https://www.mathnet.ru/eng/im1845https://doi.org/10.1070/IM1979v013n01ABEH002012 https://www.mathnet.ru/eng/im/v42/i4/p773
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Abstract page: | 400 | Russian version PDF: | 124 | English version PDF: | 13 | References: | 93 | First page: | 1 |
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