2020/06/01 by Emanuel Carneiro, Carneiro, Emanuel, Oscar E. Quesada-Herrera +1
Mathematics · Medicine · Physics and Astronomy · #42B10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2006.00959
openalex publication_date 2020/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a generalized version of the sign uncertainty principle for the Fourier transform, first proposed by Bourgain, Clozel and Kahane in 2010 and revisited by Cohn and Gonçalves in 2019. In our setup, the signs of a function and its Fourier transform resonate with a generic given function P outside of a ball. One essentially wants to know if and how soon this resonance can happen, when facing a suitable competing weighted integral condition. The original version of the problem corresponds to the case P ≡ 1. Surprisingly, even in such a rough setup, we are able to identify sharp constants in some cases.