Orthonormal Expansions for Translation-Invariant Kernels

Filip Tronarp; Toni Karvonen

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arXiv · 2206.08648

Orthonormal Expansions for Translation-Invariant Kernels

Filip Tronarp·Toni Karvonen

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Abstract

We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of $\mathscr{L}_2(\mathbb{R})$. This allows us to derive explicit expansions on the real line for (i) Mat\'ern 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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BibTeX RIS

Filip Tronarp, Toni Karvonen. 2022-06-17. Orthonormal Expansions for Translation-Invariant Kernels. https://arxiv.org/abs/2206.08648

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