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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:
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
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Full Text: DOI
References:
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