2022/06/17 by Filip Tronarp, Toni Karvonen, Tronarp, Filip +1 · 1 citation
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Elasticity and Material Modeling #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.2206.08648
openalex publication_date 2022/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of \mathscrL2(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.