Autour d'un problème extrémal étudié par Edmund Landau

Abstract

This expository article is an introduction to Landau's problem of bounding the derivative, knowing bounds for the function and its second derivative, and some of its variants and generalizations. Connexions with convex and functional analysis, numerical integration, and approximation theory are emphasized. Among others, we describe the set of extreme points of the relevant set of functions.

arXiv commentin French. Sections 7.6 and 7.7 have been rewritten. The Graduate Journal of Mathematics, Mediterranean Institute for the Mathematical Sciences (MIMS), A para{î}tre