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

This paper considers the problem of n-widths of a Sobolev function class . r. determined by P r (D) = D . . l j=1(D 2 .t 2 j 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 . = 0 or . = 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.