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

[摘要] Let I be a finite interval, r is an element of N and p(t) = dist {t, partial derivativeI}, t is an element of I. Denote by Delta', W-p,alpha(r), 0 less than or equal to alpha < infinity, the class of functions x on I with the seminorm. parallel tox((r)) rho(alpha)parallel toL(p) less than or equal to 1 for which Delta(tau)(s)x, tau > 0, is nonnegative on I. We obtain two-sided estimates of the Kolmogorov widths d(n)(Delta(+)(s)W(p,alpha)(r))L-q and of the linear widths d(n)(Delta(+)(s)W(p,alpha)(r))L-lin(q), s = 0, 1,..., r + 1. (C) 2001 Academic Press.

[发布日期] 2001-12-01

[关键词] widths of Sobolev-type classes;Kolmogorov widths;linear widths