74 citations · 275 across the 23 of their papers we have counts for
13 papers · 1 filter
Schwartz-Class Gabor Windows and the Balian-Low Classification
Andrei Caragea, Götz Pfander
A lattice Gabor frame consists of a window function and its time-frequency shifts along a lattice. We classify the lattices that admit Schwartz-class and, equivalently, Feichtinger…
Tilings, packings, and the existence of Schwartz-class Gabor windows
Andrei Caragea, Mihail N. Kolountzakis, Götz Pfander
The existence and construction of Schwartz-class windows for lattice Gabor frames is a central problem in time--frequency analysis. For general time--frequency lattices, we charact…
The normalized orbit of a bounded normal operator can be a frame
Ilya A. Krishtal, Götz E. Pfander
Conjecture 3 in [A. Aldroubi, C. Cabrelli, I. Krishtal, and U. Molter, Dynamical Sampling: A Survey, La Matematica 5 (2026), Article 37] postulates that for any bounded normal oper…
Prony's Method in Banach Modules
Ilya A. Krishtal, Götz E. Pfander
We show that the classical Prony's method for recovery of a sparse signal from its consecutive Fourier coefficients can be viewed as a spectral identification problem for an unknow…
Quantitative approximation results for complex-valued neural networks
A. Caragea, D. G. Lee, J. Maly +2
Until recently, applications of neural networks in machine learning have almost exclusively relied on real-valued networks. It was recently observed, however, that complex-valued n…
A Balian-Low Theorem for Subspaces
A. Caragea, D. Lee, G. E. Pfander +1
We extend the Balian-Low theorem to Gabor subspaces of by involving the concept of additional time-frequency shift invariance. We prove that if a Gabor system on a…