2014/05/13 by B. G. Giraud, Bertrand G. Giraud, Giraud, Bertrand G. +2 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Mathematics and Applications #Matrix Theory and Algorithms #Nuclear Theory (nucl-th) #hep-ph #hep-th #math-ph #math.MP #nucl-th
paper · pdf · doi:10.48550/arxiv.1405.3155
12 pages, 9 figures (in 4 groups)
arxiv created 2014/05/13 · openalex publication_date 2014/05/13 · arxiv updated 2014/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Characterizing in a constructive way the set of real functions whose Fourier transforms are positive appears to be yet an open problem. Some sufficient conditions are known but they are far from being exhaustive. We propose two constructive sets of necessary conditions for positivity of the Fourier transforms and test their ability of constraining the positivity domain. One uses analytic continuation and Jensen inequalities and the other deals with Toeplitz determinants and the Bochner theorem. Applications are discussed, including the extension to the two-dimensional Fourier-Bessel transform and the problem of positive reciprocity, i.e. positive functions with positive transforms.