Orthonormal expansions for translation-invariant kernels
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/61eb9139-fd32-4e86-a249-65f01681842c
- author
- Tronarp, Filip LU and Karvonen, Toni
- organization
- publishing date
- 2024-09
- 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}}, }