TY - JOUR
T1 - Orthonormal expansions for translation-invariant kernels
AU - Tronarp, Filip
AU - Karvonen, Toni
PY - 2024/9
Y1 - 2024/9
N2 - 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.
AB - 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.
KW - Orthogonal polynomials
KW - Orthonormal expansions
KW - Positive-definite kernels
KW - Radial basis functions
U2 - 10.1016/j.jat.2024.106055
DO - 10.1016/j.jat.2024.106055
M3 - Article
AN - SCOPUS:85195883067
SN - 0021-9045
VL - 302
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
M1 - 106055
ER -