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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.
94A20Sampling theory
42B10Fourier type transforms, several variables
46E22Hilbert spaces with reproducing kernels
68Q32Computational learning theory
68T05Learning and adaptive systems
68U10Image processing (computing aspects)
41A05Interpolation (approximations and expansions)
62J05Linear regression