Autour d'un problème extrémal étudié par Edmund Landau

Michel Balazard (1)

1 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: Landau inequality; Extremal problems; Kolmogorov inequality; extreme points; Peano kernel; Euler splines

Domaines: Analyse classique [math.CA]

Michel Balazard. Autour d'un problème extrémal étudié par Edmund Landau. The Graduate Journal of Mathematics, 2020, 5 (2), pp.88-110. ⟨hal-02612068v2⟩