Smale, Steve; Zhou, Ding-Xuan Shannon sampling and function reconstruction from point values. (English) Zbl 1107.94007 Bull. Am. Math. Soc., New Ser. 41, No. 3, 279-305 (2004). This important paper constructs a new framework for understanding Shannon’s sampling theorem and throws light on the relations among sampling theory, learning theory and statistics. It proposes a measure of the richness of the data, which is used to substitute the bandwidth in standard sampling theorem, so that the error of reconstructing a signal from observed noised data is analyzed in a novel method. Reviewer: Qiao Wang (Nanjing) Cited in 1 ReviewCited in 122 Documents MSC: 94A20 Sampling theory in information and communication theory 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 68T05 Learning and adaptive systems in artificial intelligence 68U10 Computing methodologies for image processing 41A05 Interpolation in approximation theory 62J05 Linear regression; mixed models Keywords:sampling theorem; interpolation; regularization method; learning theory; kernel function PDFBibTeX XMLCite \textit{S. Smale} and \textit{D.-X. Zhou}, Bull. Am. Math. Soc., New Ser. 41, No. 3, 279--305 (2004; Zbl 1107.94007) Full Text: DOI References: [1] Akram Aldroubi, Non-uniform weighted average sampling and reconstruction in shift-invariant and wavelet spaces, Appl. Comput. Harmon. 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