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A Primer on Reproducing Kernel Hilbert Spaces
Author(s): Jonathan H. Manton;Pierre-Olivier Amblard
Source: Journal:Foundations and Trends® in Signal Processing ISSN Print:1932-8346, ISSN Online:1932-8354 Publisher:Now Publishers Volume 8 Number 1-2, Pages: 126(1-126) DOI: 10.1561/2000000050 Keywords: Reproducing Kernel Hilbert Spaces
Abstract:
Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material,
greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and explaining when and why these spaces are efficacious.
The novel viewpoint is that reproducing kernel Hilbert space theory studies extrinsic geometry, associating with each geometric configuration a canonical
overdetermined coordinate system. This coordinate system varies continuously with changing geometric configurations, making it well-suited for studying
problems whose solutions also vary continuously with changing geometry. This primer can also serve as an introduction to infinite-dimensional linear algebra
because reproducing kernel Hilbert spaces have more properties in common with Euclidean spaces than do more general Hilbert spaces.
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