| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4614059 | Journal of Mathematical Analysis and Applications | 2017 | 16 Pages |
Abstract
We study sharp frame bounds of Gabor frames for integer redundancy with the standard Gaussian window and prove that the square lattice optimizes both the lower and the upper frame bound among all rectangular lattices. This proves a conjecture of Floch, Alard & Berrou (as reformulated by Strohmer & Beaver). The proof is based on refined log-convexity/concavity estimates for the Jacobi theta functions θ3θ3 and θ4θ4.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Markus Faulhuber, Stefan Steinerberger,