Kolmogorov and Linear Widths of Weighted Sobolev-Type Classes on a Finite Interval, II

AbstractLet I be a finite interval, r∈N and ρ(t)=dist{t, ∂I}, t∈I. Denote by Δs+Wrp, α, 0⩽α<∞, the class of functions x on I with the seminorm ‖x(r)ρα‖Lp⩽1 for which Δsτx, τ>0, is nonnegative on I. We obtain two-sided estimates of the Kolmogorov widths dn(Δs+Wrp, α)Lq and of the linear widths dn(Δs+Wrp, α)linLq, s=0, 1, …, r+1