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

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