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Asymptotic formulas for $n$-diameters of certain compacta in $L_2[0,1]$
Kh. Nasyrova Tashkent State University
Abstract:
In the current article the order of the Kolmogorov $n$-diameters of compacta, determined by the operators
$$
Ly=p(x)\frac{dy}{dx}+q(x)y,\quad Ly=\Bigl[-\frac{d^2}{dx^2}+q(x)\frac d{dx}\Bigr]^ry
$$
in $L_2[0,1]$ with a bound on the order of the error is studied and asymptotic formulas for $d_n$ as a function of $p(x)$, $g(x)$ and $r$ are derived.
Received: 24.12.1974
Citation:
Kh. Nasyrova, “Asymptotic formulas for $n$-diameters of certain compacta in $L_2[0,1]$”, Mat. Zametki, 20:3 (1976), 331–340; Math. Notes, 20:3 (1976), 745–750
Linking options:
https://www.mathnet.ru/eng/mzm7851 https://www.mathnet.ru/eng/mzm/v20/i3/p331
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