, Volume 45, Issue 3, pp 269-299

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.

Submitted: August 17, 2001¶ Revised: November 5, 2001.