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On \(n\)-widths of a Sobolev function class in Orlicz spaces. (English) Zbl 1323.41025

Summary: This paper considers the problem of \(n\)-widths of a Sobolev function class \(\Omega_\infty^r\) determined by \(P_r(D)=D^\sigma \prod_{j=1}^l(D^2-t_j^2I)\) in Orlicz spaces. The relationship between the extreme value problem and width theory is revealed by using the methods of functional analysis. Particularly, as \(\sigma = 0\) or \(\sigma = 1\), 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.

MSC:

41A30 Approximation by other special function classes
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
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