A sharp bound for sampling widths in the uniform norm: kernel $D$-optimal designs and oversampling

Sebastian Neumayer, Tino Ullrich

For every reproducing kernel Hilbert space ${\mathcal{H}}_K$ with bounded kernel $K$, we prove that the linear sampling widths $g_m^{\text{lin}}$ and Gelfand widths $c_n$ in the unif…