Inequalities between s-numbers and n-width

Abstract: We prove that all s-numbers can be bounded by each other with a factor $e(n+1)$. This is sharp up to the constant and settles conjectures of Mityagin, Henkin, Carl and Pietsch dating back to 1963. We also extend it to widths of convex sets and discuss optimality there, as well as applications to the adaption problem in information-based complexity.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

Function spaces