Analysis Seminar

Mathias Sonnleitner, University of Passau

Covering completely symmetric convex bodies

A completely symmetric convex body is invariant under reflections or permutations of coordinates. We can bound its metric entropy numbers and consequently its mean width using sparse approximation. We provide an extension to quasi-convex bodies and present an application to unit balls of Lorentz spaces, where we can provide a complete picture of the rich behavior of entropy numbers. These spaces are compatible with sparse approximation and arise from interpolation of Lebesgue sequence spaces, for which a similar result is by now classical. Based on joint work with J. Prochno and J. Vybiral.

MC5403