Integral Equations and Operator Theory

, Volume 45, Issue 3, pp 269–299 | Cite as

Asymptotic Estimates for Interpolation and Constrained Approximation in \( H^{2} \) by Diagonalization of Toeplitz Operators

  • Laurent Baratchart
  • José Grimm
  • Juliette Leblond
  • Jonathan R. Partington
Research article

Abstract.

Sharp convergence rates are provided for interpolation and approximation schemes in the Hardy space \( H^{2} \) that use band-limited data. By means of new explicit formulae for the spectral decomposition of certain Toeplitz operators, sharp estimates for Carleman and Krein-Nudel'man approximation schemes are derived. In addition, pointwise convergence results are obtained. An illustrative example based on experimental data from a hyperfrequency filter is provided.

Keywords. ((no keywords)).¶ Mathematics Subject Classification (2000). 30D55, 30E10, 42A05, 47B35, 65E05. 

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Copyright information

© Birkhäuser Verlag, Basel 2003

Authors and Affiliations

  • Laurent Baratchart
    • 1
  • José Grimm
    • 1
  • Juliette Leblond
    • 1
  • Jonathan R. Partington
    • 1
  1. 1.INRIA & School of Mathematics, BP 93 & University of Leeds, 06902 Sophia-Antipolis Cedex, France & Leeds LS2 9JT, U.K. E-mail: Juliette.Leblond@sophia.inria.frGB

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