34 citations · 111 across the 25 of their papers we have counts for
15 papers · 1 filter
The frame set of the first Hermite function
Markus Faulhuber, Philipp Petersen
We determine the frame set of the first Hermite function, thereby proving a conjecture of Lyubarskii and Nes. A characterization of semi-regular Gabor frames due to Gröchenig, Rome…
Linear dependence of time-frequency shifts of a Schwartz function
Markus Faulhuber, Philipp Petersen, Jordy Timo van Velthoven +1
We show that a finite number of time-frequency shifts of a Schwartz function can be linearly dependent. This disproves the so-called HRT conjecture of Heil, Ramanathan, and Topiwal…
Operator-isomorphism pairs and Zak transform methods for the study of Gabor systems
Markus Faulhuber
We collect and summarize results on the unitary equivalence of Gabor systems by pairs of unitary operators and global isometries. The methods are then used to study Gabor systems w…
Gabor systems with Hermite functions of order n and oversampling greater than n+1 which are not frames
Markus Faulhuber
We show that a sufficient density condition for Gabor systems with Hermite functions over lattices is not sufficient in general. This follows from a result on how zeros of the Zak…
On the frame property of Hermite functions and exploration of their frame sets
Markus Faulhuber, Irina Shafkulovska, Ilya Zlotnikov
We study Gabor frames with Hermite window functions. Gröchenig and Lyubarskii provided a sufficient density condition for their frame sets, which leads to what we call the "safety…
Gabor frame bound optimizations
Markus Faulhuber, Irina Shafkulovska
We study sharp frame bounds of Gabor systems over rectangular lattices for different windows and integer oversampling rate. In some cases we obtain optimality results for the squar…
Time-Frequency Analysis (Lecture Notes)
Markus Faulhuber
These lecture notes accompanied the course Time-Frequency Analysis given at the Faculty of Mathematics of the University of Vienna in the summer term 2021. The material is suitable…
The Strohmer and Beaver Conjecture for Gaussian Gabor Systems - A Deep Mathematical Problem (?)
Markus Faulhuber
In this article we are going to discuss the conjecture of Strohmer and Beaver for Gaussian Gabor systems. It asks for an optimal sampling pattern in the time-frequency plane, where…
On the Parity under Metapletic Operators and an Extension of a Result of Lyubarskii and Nes
Markus Faulhuber
In this work we show that if the frame property of a Gabor frame with window in Feichtinger's algebra and a fixed lattice only depends on the parity of the window, then the lattice…
Some curious results related to a conjecture of Strohmer and Beaver
Markus Faulhuber
We study results related to a conjecture formulated by Strohmer and Beaver about optimal Gaussian Gabor frame set-ups. Our attention will be restricted to the case of Gabor systems…
A Short Note on the Frame Set of Odd Functions
Markus Faulhuber
In this work we derive a simple argument which shows that Gabor systems consisting of odd functions of variables and symplectic lattices of density cannot constitute a Ga…
Multi-Window Weaving Frames
Monika Dörfler, Markus Faulhuber
In this work we deal with the recently introduced concept of weaving frames. We extend the concept to include multi-window frames and present the first sufficient criteria for a fa…
Minimal Operator Norms via Minimal Theta Functions
Markus Faulhuber
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…
Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions
Markus Faulhuber, Stefan Steinerberger
We study sharp frame bounds of Gabor frames with the standard Gaussian window and prove that the square lattice optimizes both the lower and the upper frame bound among all rectang…
Gabor Frame Sets of Invariance - A Hamiltonian Approach to Gabor Frame Deformations
Markus Faulhuber
In this work we study families of pairs of window functions and lattices which lead to Gabor frames which all possess the same frame bounds. To be more precise, for every generaliz…