Orthonormal Expansions for Translation-Invariant Kernels

06/17/2022

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by   Filip Tronarp, et al.

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We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of ℒ_2(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.