Minimal Operator Norms via Minimal Theta Functions

Abstract

We investigate sharp frame bounds of Gabor frames with chirped Gaussians and rectangular lattices or, equivalently, the case of the standard Gaussian and general lattices. We prove that for even redundancy and standard Gaussian window the hexagonal lattice minimizes the upper frame bound using a result by Montgomery on minimal theta functions.

14 pages

References in corpus (2)

• Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions
• Gabor Frame Sets of Invariance - A Hamiltonian Approach to Gabor Frame Deformations

Cited by in corpus (11)

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• An Extremal Property of the Hexagonal Lattice
• Some curious results related to a conjecture of Strohmer and Beaver
• Gaussian Distributions and Phase Space Weyl--Heisenberg Frames
• Gabor frame bound optimizations
• A variational principle for Gaussian lattice sums
• Additive Stability of Frames
• The AGM of Gauss, Ramanujan's corresponding theory, and spectral bounds of self-adjoint operators