Shannon sampling. II: Connections to learning theory. (English) Zbl 1107.94008

Smale, Steve; Zhou, Ding-Xuan

Appl. Comput. Harmon. Anal. 19, No. 3, 285-302 (2005).

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.

Reviewer: Qiao Wang (Nanjing)

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

Keywords:

sampling theorem; learning theory; reproducing kernel Hilbert space; frame; function reconstruction

Citations:

Zbl 1107.94004

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