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

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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.

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Authors and Affiliations

  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.fr, , , , , , GB

    Laurent Baratchart, José Grimm, Juliette Leblond & Jonathan R. Partington

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  1. Laurent Baratchart
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  2. José Grimm
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  3. Juliette Leblond
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  4. Jonathan R. Partington
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Submitted: August 17, 2001¶ Revised: November 5, 2001.

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Baratchart, L., Grimm, J., Leblond, J. et al. Asymptotic Estimates for Interpolation and Constrained Approximation in \( H^{2} \) by Diagonalization of Toeplitz Operators. Integr. equ. oper. theory 45, 269–299 (2003). https://doi.org/10.1007/s000200300005

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  • DOI: https://doi.org/10.1007/s000200300005

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