The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

On Singular Numbers of Hankel Matrices of Markov Functions


Vasily A. Prokhorov

Department of Mathematics and Statistics,
University of South Alabama,
Mobile, Alabama 36688-0002,


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 σkn,n of the Hankel matrix Dn, where kn/n→θ∈[0,1] as n→∞. Moreover, we obtain asymptotics of the Kolmogorov, Gelfand and linear k-widths, k=kn, of the unit ball An,2 of Pn∩L2(Γ) in the space L2(μ,E), where Γ={z:|z|=1} and Pn is the class of all polynomials of the degree at most n.


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