Principe d’Heisenberg et fonctions positives

Abstract

We consider a natural problem concerning Fourier transforms. In one variable, one seeks functions f and f ^, both positive for ∣x∣≥a and vanishing at 0. What is the lowest bound for a ? In higher dimension, the same problem can be posed by replacing the interval by a ball of radius a. We show that there is indeed a strictly positive lower bound, which is estimated as a function of the dimension. In the last section the question, and its solution, are shown to be naturally related to the theory of zêta-functions.

Locations

• French digital mathematics library (Numdam) - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF
• DataCite API - View
• Annales de l’institut Fourier - View - PDF