Orthonormal Expansions for Translation-Invariant Kernels

  title={Orthonormal Expansions for Translation-Invariant Kernels},
  author={Filip Tronarp and Toni Karvonen},
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. 

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