Paper Title:

On Singular Numbers of Hankel Matrices of Markov Functions

Author(s):

Vasily A. Prokhorov

Department of Mathematics and Statistics,
University of South Alabama,
Mobile, Alabama 36688-0002,
USA.
E-mail: prokhoro@southalabama.edu
URL: http://www.southalabama.edu/mathstat/people/prokhorov.shtml

Abstract:

Let E ⊂ (01,1) be a compact set and let μ be a positive Borel measure with support supp μ=E. Let

In the case when E=[a,b]⊂ (-1,1) and μ satisfies the condition dμ/dx>0 a.e. on E, we investigate asymptotic behavior of singular numbers σ_kn,n of the Hankel matrix D_n, where k_n/n→θ∈[0,1] as n→∞. Moreover, we obtain asymptotics of the Kolmogorov, Gelfand and linear k-widths, k=k_n, of the unit ball A_n,2 of P_n∩L₂(Γ) in the space L₂(μ,E), where Γ={z:|z|=1} and P_n is the class of all polynomials of the degree at most n.

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