Localization operator based on sampling multipliers
The paper studies the localization operator based on sampling multipliers. The obtained explicit error bounds for approximation in the Paley-Wiener spaces unify several extensions of the Shannon sampling theorem and generalize the localized sampling with special sampling multipliers. By applying the Hermite multiplier in the localized sampling series, exponentially decaying accuracy can be achieved for approximating functions and their derivatives in Paley-Wiener spaces, and practical means for choosing parameters to achieve any desired accuracy for sampling is provided. The localized sampling series significantly improves the convergence rate of sampling expansion in Mayer wavelet subspaces when the Hermite multipliers are used. Numerical experiments are presented to demonstrate the high accuracy performed by using the localized sampling series.
scientific article; zbMATH DE number 5131621