Research article

Integral Equations and Operator Theory

, Volume 45, Issue 3, pp 269-299

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

  • Laurent BaratchartAffiliated withINRIA & School of Mathematics, BP 93 & University of Leeds, 06902 Sophia-Antipolis Cedex, France & Leeds LS2 9JT, U.K. E-mail: Juliette.Leblond@sophia.inria.fr
  • , José GrimmAffiliated withINRIA & School of Mathematics, BP 93 & University of Leeds, 06902 Sophia-Antipolis Cedex, France & Leeds LS2 9JT, U.K. E-mail: Juliette.Leblond@sophia.inria.fr
  • , Juliette LeblondAffiliated withINRIA & School of Mathematics, BP 93 & University of Leeds, 06902 Sophia-Antipolis Cedex, France & Leeds LS2 9JT, U.K. E-mail: Juliette.Leblond@sophia.inria.fr
  • , Jonathan R. PartingtonAffiliated withINRIA & School of Mathematics, BP 93 & University of Leeds, 06902 Sophia-Antipolis Cedex, France & Leeds LS2 9JT, U.K. E-mail: Juliette.Leblond@sophia.inria.fr

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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.