3 problems

Laplacian and Matérn kernel conjecture. The assumptions of part (i) are also true for the Laplacian and Matérn kernels when $C=1$.

Sampling-error conjecture. For high-dimensional problems, sampling errors exceed discretization errors.

Let $d\geqslant2$, and consider the higher-dimensional analogue of the class ${\cal F}_{s,R,M}$ of indicator functions with regular boundaries. Uniform piecewise constant approxima…