Kolmogorov and Linear Widths of Weighted Sobolev-Type Classes on a Finite Interval, II |
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| Authors: | V N Konovalov D Leviatan |
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| Institution: | International Mathematical Center, National Academy of Sciences of Ukraine, Kiev, 01601, Ukrainef1;School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel, f2;IMI, Department of Mathematics, University of South Carolina, Columbia, South Carolina, 29208, U.S.A., f3 |
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| Abstract: | Let I be a finite interval, r
and ρ(t)=dist{t, ∂I}, tI. Denote by Δs+Wrp, α, 0α<∞, the class of functions x on I with the seminorm x(r)ραLp1 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. |
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| Keywords: | widths of Sobolev-type classes Kolmogorov widths linear widths |
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