New Sign Uncertainty Principles
Year: 2020
Type: preprint
Abstract: We prove new sign uncertainty principles which vastly generalize the recent developments of Bourgain, Clozel & Kahane and Cohn & Gonçalves, and apply our results to a variety of spaces and operators. In particular, we establish new sign uncertainty principles for Fourier and Dini series, the Hilbert transform, the discrete Fourier and Hankel transforms, spherical harmonics, and Jacobi polynomials, among others. We present numerical evidence highlighting the relationship between the discrete and continuous sign uncertainty principles for the Fourier and Hankel transforms, which in turn are connected with the sphere packing problem via linear programming. Finally, we explore some connections between the sign uncertainty principle on the sphere and spherical designs.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G8321147636
OpenAlex ID: W3013889259