Consider implementing SPDE-based kernels on finite domains.

[tillahoffmann]

Borovitskiy et al. (2020) derive the Matérn and squared exponential covariance kernels on finite domains. We instead use the naïve approach of simply considering the distance after accounting for periodic boundary conditions. This means that

• the kernels are not necessarily positive semi-definite, i.e., the Fourier transform of the kernel can have negative components
• the kernels are not necessarily non-negative, i.e., the inverse Fourier transform of the kernel can have negative values.
• the numerical FFT of the kernel and the theoretical power spectrum do not necessarily match if the number of grid points is small.

We may want to implement the (truncated) infinite summation at a future point.