Orthonormal Expansions for Translation-Invariant Kernels

arXiv:2206.08648v4 Announce Type: replace-cross
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.

abstract arxiv cs.lg cs.na fourier functions general integer kernel line math.na orders stat.ml terms translation type