Table 1.

Summary table of kernels and their spectral densities.

Kernel name	$k\left(\delta \right)$	$p\left(\omega \right)$
Squared exponential	$e^{-\frac{\left({\Vert \; \delta \Vert }_2^2\right)}{2\sigma }}$, $\sigma >0$	${\left(2\pi \right)}^{-\frac{D}{2}}{\sigma }^{D}exp(-\frac{{\sigma }^2{\Vert \; \omega \Vert }_2^2}{2})$
Laplacian	$exp(-\sigma \Vert \delta {\Vert }_1)$, $\sigma >0$	${\left(\frac{2}{\pi }\right)}^{\frac{2}{D}}{\prod }_{i=1}^D\frac{\sigma }{{\sigma }^2+{\omega }_i^2}$
Matérn	$\frac{2^{1-\lambda }}{\Gamma \left(\lambda \right)}{\left(\frac{\sqrt{\left(2\lambda \right)\Vert \delta {\Vert }_2}}{\sigma }\right)}^{\lambda }{K}_{\lambda }\left(\frac{\sqrt{\left(2\lambda \right)\Vert \delta {\Vert }_2}}{\sigma }\right)$	$\frac{2^{D+\lambda }{\pi }^{\frac{D}{2}}\Gamma (\lambda +D∕2){\lambda }^{\lambda }}{\Gamma \left(\lambda \right){\sigma }^{2\lambda }}{\left(\frac{2\lambda }{{\sigma }^2}+4{\pi }^2{\Vert \; \omega \Vert }_2^2\right)}^{-(\lambda +D∕2)}$
	$\lambda >0,\sigma >0$