Abstract:
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.
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