Localization operator based on sampling multipliers

Localization operator based on sampling multipliers is proposed to reconstruct a function in Paley–Wiener spaces by its local samples. Explicit error estimate is derived for the operator to approximate functions and their derivatives. For Hermite multipliers, exponentially decaying accuracy of approximation is achieved, and a practical criteria for the sampling to obtain any desired accuracy is provided. The estimates unify several existing results for sampling and accelerate the convergence rate of wavelet sampling series.