Geodesic
Asymptotic formulas for $n$-diameters of certain compacta in $L_2[0,1]$
Matematičeskie zametki, Tome 20 (1976) no. 3, pp. 331-340 
Kh. Nasyrova. Asymptotic formulas for $n$-diameters of certain compacta in $L_2[0,1]$. Matematičeskie zametki, Tome 20 (1976) no. 3, pp. 331-340. http://geodesic.mathdoc.fr/item/MZM_1976_20_3_a3/
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     author = {Kh. Nasyrova},
     title = {Asymptotic formulas for $n$-diameters of certain compacta in $L_2[0,1]$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {331--340},
     year = {1976},
     volume = {20},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_3_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.