2008/11/26 by Jean Bourgain, Laurent Clozel, Bourgain, Jean +3 · 1 citation
Mathematics · #11R42 #42A05 #42A38 #42B10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:11R42 #msc:42A05 #msc:42A38 #msc:42B10
paper · pdf · doi:10.48550/arxiv.0811.4360
arxiv created 2008/11/26 · arxiv updated 2009/12/01
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).