Author

T. Ullrich

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Preprint Sep 2026

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

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 uniform norm satisfy $$ g_m^{\text{lin}}(B_{\mathcal H_K})_\infty \leq \frac{m+1}{m-n+1}\, c_n(B_{\mathcal H_K})_\infty\quad , \quad m\ge n. $$...

S. Neumayer, T. Ullrich · 0 citations

Preprint Sep 2026

Greedy sampling designs via reduced basis methods: optimal recovery in the uniform norm

We study optimal sampling recovery in reproducing kernel Hilbert spaces (RKHS) in the uniform norm. For every RKHS with bounded kernel, we establish new comparisons between linear sampling widths and Gelfand widths that overcome the known square-root gap, without requiring a measure or a Christoffel-type condition. Our...

S. Neumayer, K. Pozharska, T. Ullrich · 1 citation · ⚡1