Kolmogorov and linear widths of weighted Besov classes

AbstractWe study the Kolmogorov m-widths dm(Bsα(Lτ,μ),Lp,μ) and the linear m-widths δm(Bsα(Lτ,μ),Lp,μ) of the weighted Besov classes Bsα(Lτ,μ) on [−1,1], where Lq,μ, 1⩽q⩽∞, denotes the Lq space on [−1,1] with respect to the measure (1−t2)μ−1/2dt, μ>0. Optimal asymptotic orders of dm(Bsα(Lτ,μ),Lp,μ) and δm(Bsα(Lτ,μ),Lp,μ) as m→∞ are obtained for all 1⩽p,τ⩽∞. It turns out that in many cases, the orders of dm(Bsα(Lτ,μ),Lp,μ) are significantly smaller than the corresponding orders of the best m-term approximation by ultraspherical polynomials, which is somewhat surprising