Minimal Frame Operator Norms Via Minimal Theta Functions

The Journal of Fourier Analysis and Applications
Markus Faulhuber

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.

References

Apr 22, 2015·Applied and Computational Harmonic Analysis·Maurice A de Gosson
Aug 12, 2016·Journal of Pseudo-differential Operators and Applications·Markus Faulhuber

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