Corpus ID: 235795074

# Gaussian Gabor frames, Seshadri constants and generalized Buser--Sarnak invariants

@inproceedings{Luef2021GaussianGF,
title={Gaussian Gabor frames, Seshadri constants and generalized Buser--Sarnak invariants},
author={Franz Luef and Xu Wang},
year={2021}
}
• Published 2021
• Mathematics
We investigate the frame set of regular multivariate Gaussian Gabor frames using methods from Kähler geometry such as Hörmander’s ∂-method, the Ohsawa–Takegoshi extension theorem and a Kähler-variant of the symplectic embedding theorem of McDuff-Polterovich for ellipsoids. Our approach is based on the well-known link between sets of interpolation for the Bargmann-Fock space and the frame set of multivariate Gaussian Gabor frames. We state sufficient conditions in terms of the Seshadri constant… Expand
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#### References

SHOWING 1-10 OF 64 REFERENCES
History and Evolution of the Density Theorem for Gabor Frames
The Density Theorem for Gabor Frames is one of the fundamental results of time-frequency analysis. This expository survey attempts to reconstruct the long and very involved history of this theoremExpand
Quantum Theta Functions and Gabor Frames for Modulation Spaces
• Mathematics
• 2009
Representations of the celebrated Heisenberg commutation relations in quantum mechanics (and their exponentiated versions) form the starting point for a number of basic constructions, both inExpand
Dilation of the Weyl symbol and Balian-Low theorem
• Mathematics
• 2013
The key result of this paper describes the fact that for an important class of pseudodifferential operators the property of invertibility is preserved under minor dilations of their Weyl symbols.Expand
Bargmann transform, Zak transform, and coherent states
It is well known that completeness properties of sets of coherent states associated with lattices in the phase plane can be proved by using the Bargmann representation or by using the kq Expand
Seshadri constants are local invariants, introduced by Demailly, which measure the local positivity of ample line bundles. Recent interest in Seshadri constants stems on the one hand from the factExpand
Numerical characterization of the Kahler cone of a compact Kahler manifold
• Mathematics, Physics
• 2001
The goal of this work is to give a precise numerical description of the Kahler cone of a compact Kahler manifold. Our main result states that the Kahler cone depends only on the intersection form ofExpand
Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions
• Mathematics
• 2017
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 boundExpand
Unobstructed symplectic packing for tori and hyper-Kähler manifolds
• Mathematics
• 2016
Let M be a closed symplectic manifold of volume V. We say that the symplectic packings of M by balls are unobstructed if any collection of disjoint symplectic balls (of possibly different radii) ofExpand
Gabor Frames and Totally Positive Functions
• Mathematics
• 2011
Let g be a totally positive function of finite type, i.e., ĝ(ξ) = ∏M ν=1(1 + 2πiδνξ) −1 for δν ∈ R and M ≥ 2. Then the set {eg(t − αk) : k, l ∈ Z} is a frame for L(R), if and only if αβ < 1. ThisExpand
Gabor Time-Frequency Lattices and the Wexler-Raz Identity
• Mathematics
• 1994
Gabor time-frequency lattices are sets of functions of the form $g_{m \alpha , n \beta} (t) =e^{-2 \pi i \alpha m t}g(t-n \beta)$ generated from a given function $g(t)$ by discrete translations inExpand