Complex-Analytic Approach to the Sinc-Gauss Sampling Formula

Abstract

This paper is concerned with theoretical error estimates for a sampling formula with the sinc-Gaussian kernel. Qian et al. have recently given an error estimate for the class of band-limited functions by Fourier-analytic approach. In contrast, we adopt in this paper a complex-analytic approach to derive an error estimate for a wider class of functions including unbounded functions on $\mathbf{R}$. Part of the result of Qian et al. can be derived from ours as an immediate corollary. Computational results show a fairly good agreement with our theoretical analysis.