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 onR. 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.
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Tanaka, K., Sugihara, M. & Murota, K. Complex-analytic approach to the sinc-Gauss sampling formula. Japan J. Indust. Appl. Math. 25, 209 (2008). https://doi.org/10.1007/BF03167520
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DOI: https://doi.org/10.1007/BF03167520