Geodesic
Kolmogorov Widths of Weighted Sobolev Classes on Closed Intervals
Matematičeskie zametki, Tome 84 (2008) no. 5, pp. 676-680

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In this paper, we estimate the asymptotics of the Kolmogorov widths of weighted Sobolev classes in the metric of $L_p$. We establish the relationship between the width of the set $W^1_{\infty,g}$ and the approximation of the antiderivative function $g$ by piecewise constant functions.
Keywords: Kolmogorov width, weighted Sobolev class, measurable function, the space $L_p$, Maiorov discretization, Riemann–Liouville operator. 
@article{MZM_2008_84_5_a3,
     author = {A. A. Vasil'eva},
     title = {Kolmogorov {Widths} of {Weighted} {Sobolev} {Classes} on {Closed} {Intervals}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {676--680},
     publisher = {mathdoc},
     volume = {84},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_5_a3/}
}
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A. A. Vasil'eva. Kolmogorov Widths of Weighted Sobolev Classes on Closed Intervals. Matematičeskie zametki, Tome 84 (2008) no. 5, pp. 676-680. http://geodesic.mathdoc.fr/item/MZM_2008_84_5_a3/