Rate of Convergence of Schmidt Pairs and Rational Functions Corresponding to BestApproximants of Truncated Hankel Operators

摘要

The problem of approximating Hankel operators of infinite rank by finite-tankHankel operators is considered. For efficiency, truncated infinite Hankel matrices gamma n of gamma are utilized. In this paper for any compact Hankel operator gamma of the Wiener class, we derive the rate of l sub 2-convergence of the Schmidt pairs of gamma n to the corresponding Schmidt pairs of gamma. For a certain subclass of Hankel operators of the Wiener class, we also obtain the rate of l sub 1-convergence. In addition, an upper bound for the rate of uniform convergence of the rational symbols of best rank-k Hankel approximants of gamma to the corresponding rational symbol of the best rank-k Hankel approximant to gamma as n yielding infinity is derived. Hankel norm, Rational approximation, Order of approximation Wiener class.