9 citations · 17 across the 10 of their papers we have counts for
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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…
Principal minors of Fourier matrices of square-free order
Andrei Caragea, Dae Gwan Lee, Romanos Malikiosis +1
Chebotarev's theorem on roots of unity states that all minors of a Fourier matrix are non-zero if and only if the order of the matrix is prime. We establish cases in which all prin…
On the principal minors of Fourier matrices
Andrei Caragea, Dae Gwan Lee
For the -dimensional Fourier matrix , we prove that if is square-free, then every and principal minor of is non…
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…
Neural network approximation and estimation of classifiers with classification boundary in a Barron class
Andrei Caragea, Philipp Petersen, Felix Voigtlaender
We prove bounds for the approximation and estimation of certain binary classification functions using ReLU neural networks. Our estimation bounds provide a priori performance guara…
Time-Frequency Shift Invariance of Gabor Spaces with an -Generator
Andrei Caragea, Dae Gwan Lee, Friedrich Philipp +1
We consider Gabor Riesz sequences generated by a lattice and a window function which is well localized in both time and frequency. W…
A quantitative subspace Balian-Low theorem
Andrei Caragea, Dae Gwan Lee, Friedrich Philipp +1
Let be the subspace spanned by a Gabor Riesz sequence with and a lattice of rational density.…
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…