RATE OF CONVERGENCE OF SCHMIDT PAIRS AND RATIONAL FUNCTIONS CORRESPONDING TO BEST APPROXIMANTS OF TRUNCATED HANKEL-OPERATORS
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The problem of approximating Hankel operators of infinite rank by finite-rank Hankel operators is considered. For efficiency, truncated infinite Hankel matrices n of are utilized. In this paper for any compact Hankel operator of the Wiener class, we derive the rate of l2-convergence of the Schmidt pairs of n to the corresponding Schmidt pairs of . 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 n to the corresponding rational symbol of the best rank-k Hankel approximant to as n is derived. 1992 Springer-Verlag New York Inc.