Abstract
This paper considers the problem of n-widths of a Sobolev function class Ω∞r determined by Pr(D) = Dσ Πj=1l(D2 −tj2I) in Orlicz spaces. The relationship between the extreme value problem and width theory is revealed by using the methods of functional analysis. Particularly, as σ = 0 or σ = 1, the exact values of Kolmogorov’s widths, Gelfand’s widths, and linear widths are obtained respectively, and the related extremal subspaces and optimal linear operators are given.
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