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Orthonormal expansions for translation-invariant kernels

Tronarp, Filip LU and Karvonen, Toni (2024) In Journal of Approximation Theory 302.
Abstract

We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of ℒ2(R). This allows us to derive explicit expansions on the real line for (i) Matérn kernels of all half-integer orders in terms of associated Laguerre functions, (ii) the Cauchy kernel in terms of rational functions, and (iii) the Gaussian kernel in terms of Hermite functions.

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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Orthogonal polynomials, Orthonormal expansions, Positive-definite kernels, Radial basis functions
in
Journal of Approximation Theory
volume
302
article number
106055
publisher
Elsevier
external identifiers
  • scopus:85195883067
ISSN
0021-9045
DOI
10.1016/j.jat.2024.106055
language
English
LU publication?
yes
id
61eb9139-fd32-4e86-a249-65f01681842c
date added to LUP
2024-07-02 15:01:43
date last changed
2024-07-02 15:02:21
@article{61eb9139-fd32-4e86-a249-65f01681842c,
  abstract     = {{<p>We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of ℒ<sub>2</sub>(R). This allows us to derive explicit expansions on the real line for (i) Matérn kernels of all half-integer orders in terms of associated Laguerre functions, (ii) the Cauchy kernel in terms of rational functions, and (iii) the Gaussian kernel in terms of Hermite functions.</p>}},
  author       = {{Tronarp, Filip and Karvonen, Toni}},
  issn         = {{0021-9045}},
  keywords     = {{Orthogonal polynomials; Orthonormal expansions; Positive-definite kernels; Radial basis functions}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Approximation Theory}},
  title        = {{Orthonormal expansions for translation-invariant kernels}},
  url          = {{http://dx.doi.org/10.1016/j.jat.2024.106055}},
  doi          = {{10.1016/j.jat.2024.106055}},
  volume       = {{302}},
  year         = {{2024}},
}