2020/03/24 by Felipe Gonçalves, Gonçalves, Felipe, Diogo Oliveira e Silva +3 · 1 citation
Engineering · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2003.10765
openalex publication_date 2020/03/24 · openalex created_date 2022/07/24 · openalex updated_date 2026/07/28
The sign uncertainty principle of Bourgain, Clozel & Kahane asserts that if a\nfunction f:\ℝd\→ \ℝ and its Fourier transform widehatf\nare nonpositive at the origin and not identically zero, then they cannot both\nbe nonnegative outside an arbitrarily small neighborhood of the origin. In this\narticle, we establish some equivalent formulations of the sign uncertainty\nprinciple, and in particular prove that minimizing sequences exist within the\nSchwartz class when d=1. We further address a complementary sign uncertainty\nprinciple, and show that corresponding near-minimizers concentrate a universal\nproportion of their positive mass near the origin in all dimensions.\n