Cohn-Elkies functions from Gabor frames
Yuri Manin, Matilde Marcolli
TL;DR
This paper explores the connection between sphere packing bounds and Gabor frames, presenting a method to construct Cohn-Elkies functions from Gabor frame duals with Gaussian windows in any dimension.
Contribution
It introduces a novel construction of Cohn-Elkies functions derived from Gabor frame duals, bridging two distinct mathematical areas.
Findings
New construction method for Cohn-Elkies functions from Gabor frames
Applicable in arbitrary dimensions for Gabor frames with Gaussian windows
Establishes a link between sphere packing bounds and signal analysis techniques
Abstract
We investigate the relation between two different mathematical problems: the construction of bounds on sphere packing density using Cohn-Elkies functions and the construction of Gabor frames for signal analysis. In particular, we present a general construction of Cohn-Elkies functions in arbitrary dimension, obtained from an approximate Wexel-Raz dual for Gabor frames with Gaussian window.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsPhotoacoustic and Ultrasonic Imaging · Optical and Acousto-Optic Technologies · Optical Polarization and Ellipsometry