Abstract
In this paper, we study the infinite dimensional widths and optimal recovery of Wiener–Sobolev smooth function classes WM,1(Pr(D)) determined by the r-th differential operator Pr(D) in Orlicz spaces with L(R) metric. Using tools such as the Hölder inequality, we give the exact values of the infinite dimensional Kolmogorov width and linear width of WM,1(Pr(D)) in L(R) metric. We also study the related optimal recovery problem.
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