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Relative infinite-dimensional width of Sobolev classes. (English) Zbl 1205.46018
Summary: In order to consider the problems of relative width of Sobolev classes ${W}_{p}^{r}$ on $ℝ$ in ${L}_{p}$, we propose the definition of relative infinite-dimensional width which combines the ideas of the relative width and the infinite-dimensional width. We determine the exact values of relative infinite-dimensional width for $r=1$, $p=1$ or $p=\infty$ and for $r\in ℕ$, $p=2$.
##### MSC:
 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
##### References:
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