Geodesic
A Complete Description of the Relative Widths of Sobolev Classes in the Uniform Metric
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 137-142

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We consider the width of the Sobolev class of $2\pi$-periodic functions with ${\|f^{(r)}\|_\infty\le 1}$ with respect to the set of functions $g$ such that $\|g^{(r)}\|_\infty\le M$ in the uniform metric $K_n:=K_n(W^r_\infty,MW^r_\infty,L_\infty)$. We prove a lower bound on $K_n$ for $M=1+\varepsilon$ with small $\varepsilon$. This bound together with earlier results completes the analysis of the behavior of $K_n$.
Keywords: Kolmogorov and relative widths. 
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     title = {A {Complete} {Description} of the {Relative} {Widths} of {Sobolev} {Classes} in the {Uniform} {Metric}},
     journal = {Trudy Instituta matematiki i mehaniki},
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Yu. V. Malykhin. A Complete Description of the Relative Widths of Sobolev Classes in the Uniform Metric. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 137-142. http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a12/