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Shannon sampling. II: Connections to learning theory. (English) Zbl 1107.94008
This paper continues the authors’ former study [Bull. Am. Math. Soc., New Ser. 41, No. 3, 279–305 (2004; Zbl 1107.94004)]. They propose a reproducing kernel Hilbert space (the traditional band-limited functions space is also a RKHS) framework to understand the function reconstruction beyond point evaluation. A unified framework for sampling theory and learning theory is initially established in this paper.

MSC:
94A20 Sampling theory in information and communication theory
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
68Q32 Computational learning theory
68T05 Learning and adaptive systems in artificial intelligence
68U10 Computing methodologies for image processing
41A05 Interpolation in approximation theory
62J05 Linear regression; mixed models
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References:
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