On n-widths of a Sobolev function class in Orlicz spaces

This paper considers the problem of n-widths of a Sobolev function class Ω_∞^r determined by P_r(D) = D^σ∏_j=1^l(D²-t_j² I) 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.