Entropy numbers of spheres in Banach and quasi-Banach spaces

Abstract

We prove sharp upper bounds on the entropy numbers $e_k(S_p^{d-1},{\ell }_q^d)$ of the $p$-sphere in ${\ell }_q^d$ in the case $k\ge d$ and $0<p\le q\le \infty$. In particular, we close a gap left open in recent work of the second author, T. Ullrich and J. Vybiral. We also investigate generalizations to spheres of general finite-dimensional quasi-Banach spaces.

References in corpus (1)

• Entropy and sampling numbers of classes of ridge functions