Rate of convergence of schmidt pairs and rational functions corresponding to best approximants of truncated hankel operators Academic Article uri icon


  • 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 as n → ∞ is derived. © 1992 Springer-Verlag New York Inc.

author list (cited authors)

  • Chui, C. K., Li, X., & Ward, J. D.

citation count

  • 4

publication date

  • March 1992