Principe d'Heisenberg et fonctions positives

Details Principe d'Heisenberg et fonctions positives Principe d'Heisenberg et fonctions positives

2008-11-26

arxiv.org/abs/0811.4360v1

Mathematics

Classical Analysis and ODEs

Scientific paper

Starting from a problem in number theory, the article investigates the properties of the couples of Fourier transforms on the real line, f and g, real and even, f >= 0 out of an interval (-a, a) and f(0) < 0, g >= 0 out of an interval (-b, b) and g(0) < 0 . How small the product ab can be ? There is a strictly positive lower bound, the exact value is not known. The same problem is considered in several dimensions (where it is related to number theory, as the article points out).

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