Geodesic
Widths of a class of analytic functions
Sbornik. Mathematics, Tome 45 (1983) no. 2, pp. 283-289 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $H^2$ be the Hardy class in the unit disk, $T_r$ the circle of radius $r$ ($0) about zero, and $\alpha$ a finite Borel measure on $~T_r$. Denote by $d_n(\alpha)$ the Kolmogorov $n$th-width of the unit ball of $~H^2$ in the metric of $L_2(T_r,\alpha)$. It is proved that $$ \lim_{n\to\infty}d_n(\alpha)r^{\frac1{2}-n}=\sqrt{g(\alpha)}, $$ where $g(\alpha)$ is the geometric mean of $\alpha$ over $T_r$. The exact values of the diameters are computed for certain measures. Bibliography: 6 titles. 
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O. G. Parfenov. Widths of a class of analytic functions. Sbornik. Mathematics, Tome 45 (1983) no. 2, pp. 283-289. http://geodesic.mathdoc.fr/item/SM_1983_45_2_a8/

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