Publication at Faculty of Mathematics and Physics |
2020
Abstract
Entropy numbers and covering numbers of sets and operators are well known geometric notions, which found many applications in various fields of mathematics, statistics, and computer science. Their values for finite-dimensional embeddings id : l(p)(n) -> l(q)(n), 0 < p, q <= infinity, are known (up to multiplicative constants) since the pioneering work of Schutt in 1984, with later improvements by Edmunds and Triebel, Kuhn and Guedon and Litvak.
The aim of this survey is to give a self-contained presentation of the result and an overview of the different techniques used in its proof. (C) 2019 Elsevier GmbH. All rights reserved.