Rate of convergence of schmidt pairs and rational functions corresponding to best approximants of truncated hankel operators

Abstract

The problem of approximating Hankel operators of infinite rank by finite-rank Hankel operators is considered. For efficiency, truncated infinite Hankel matrices Γⁿ of Γ are utilized. In this paper for any compact Hankel operator Γ of the Wiener class, we derive the rate of l₂-convergence of the Schmidt pairs of Γⁿ to the corresponding Schmidt pairs of Γ. For a certain subclass of Hankel operators of the Wiener class, we also obtain the rate of l₁-convergence. In addition, an upper bound for the rate of uniform convergence of the rational symbols of best rank-k Hankel approximants of Γⁿ to the corresponding rational symbol of the best rank-k Hankel approximant to Γ asn → ∞ is derived.