Kolmogorov and linear widths of weighted Sobolev-type classes on a finite interval

摘要

Let I be a finite interval, rε N and p(t)=dist{t,∂I}, tεI. Denote by W r p ,α, 0<α<∞, the class of functions x on I with the seminorm ∥x (r) p α∥Lp≤1. We obtain two-sided estimates of the Kolmogorov widths d n(Wr p, α)Lq and of the linear widths d n(Wr p,α)Lq lin