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arXiv · 1606.05500

A Short Note on the Comparison of Interpolation Widths, Entropy Numbers, and Kolmogorov Widths

Ingo Steinwart
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Abstract

We compare the Kolmogorov and entropy numbers of compact operators mapping from a Hilbert space into a Banach space. We then apply these general findings to embeddings between reproducing kernel Hilbert spaces and $L_\infty(\mu)$. Here we provide a sufficient condition for a gap of the order $n^{1/2}$ between the associated interpolation and Kolmogorov $n$-widths. Finally, we show that in the multi-dimensional Sobolev case, this gap actually occurs between the Kolmogorov and approximation widths.

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Ingo Steinwart. 2016-06-17. A Short Note on the Comparison of Interpolation Widths, Entropy Numbers, and Kolmogorov Widths. https://arxiv.org/abs/1606.05500

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