Abstract
The concepts of three ∞-widths are proposed and some of their properties are studied in this paper. The main result is that we obtain the exact values of the three ∞-widths of Sobolev function classes B r p( R ) in L p( R ) (1 ⩽ p ⩽ ∞) and find the optimal subspaces and the optimal linear operator. An application of the ∞-widths to optimal recovery is given. New extremal properties of cardinal splines and cardinal spline interpolation are discovered.
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