6 papers
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…
On a fundamental barrier of the Wirtinger criterion for Gabor systems with odd functions
Markus Faulhuber
We show that the Wirtinger criterion cannot be used to investigate the frame set conjecture for the first Hermite function. More generally, for odd functions, it cannot determine r…
The polarization problem for the honeycomb structure
Markus Faulhuber
We study the polarization problem in dimension 2 for the honeycomb structure and compare it to the maximal polarization lattice, the hexagonal lattice. As expected, the hexagonal l…
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…
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…