JAMING, Philippe

Métadonnées

Licence d’utilisation du document

JAMING, Philippe
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Institut de Mathématiques de Bordeaux [IMB]

Langue

Article de revue

Ce document a été publié dans

Annales de l'Institut Fourier. 2011, vol. 61, p. 53-77

Association des Annales de l'Institut Fourier

Résumé en anglais

Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the $L^2$ behavior of a Fourier transform of a function over a small set is controlled by the $L^2$ behavior of the Fourier transform of its symmetric decreasing rearrangement. In the $L^1$ case, the same is true if we further assume that the function has a support of finite measure. As a byproduct, we also give a simple proof and an extension of a result of Lieb about the smoothness of a rearrangement. Finally, a straightforward application to solutions of the free Shrödinger equation is given.< Réduire

Mots clés en anglais

Fourier transform

rearrangement inequalities

Bessel functions

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191601

Project ANR

Analyse Harmonique et Problèmes Inverses - ANR-07-BLAN-0247

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251