Autour d'un probl\`eme extr\'emal \'etudi\'e par Edmund Landau
Michel Balazard (I2M)

TL;DR
This paper introduces Landau's problem of bounding derivatives based on function bounds, exploring its variants and connections to convex analysis, numerical integration, and approximation theory.
Contribution
It provides an exposition on Landau's derivative bounding problem, highlighting its variants, generalizations, and the structure of extremal functions.
Findings
Characterization of extremal functions
Connections to convex and functional analysis
Insights into derivative bounds and their applications
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFunctional Equations Stability Results · Advanced Optimization Algorithms Research · Mathematical Inequalities and Applications
