On Blaschke products associated with n-widths

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Abstract

Let E be a closed subset of the open unit disk G={z:|z|<1}, and let μ be a positive Borel measure with support supp μ=E. Denote by Ap the restriction on E of the closed unit ball of the Hardy space Hp(G), 1⩽p⩽∞. In this paper we investigate orthogonality properties of the extremal functions associated with the Kolmogorov, Gelfand, and linear n-widths of Ap in Lq(μ,E), 1⩽q<∞, qp.

Keywords

n-widths
Blaschke product
Orthogonal polynomial
Meromorphic approximation

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1

The research of these authors was supported, in part, by NSF-INRIA collaborative research Grant INT-9732631 as well as (for E.B. Saff) by NSF research Grant DMS-0296026.