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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 $\Bbb R$ 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 $r \in \Bbb N$, $p=2$.

46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
41A46Approximation by arbitrary nonlinear expressions; widths and entropy
Full Text: DOI
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