Autour d'un problème extrémal étudié par Edmund Landau

Michel Balazard

Published 2020-05-19Version 1

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.