A. Caragea

activity

20182026

most citedA note on exponential Riesz bases

9 citations · 17 across the 10 of their papers we have counts for

collaborators

11 papers

math.FA2026

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…

math.FA2026

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…

math.FA2025

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…

math.MG2025

Minkowski chirality: a measure of reflectional asymmetry of convex bodies

Andrei Caragea, Katherina von Dichter, Kurt Klement Gottwald +3

Using an optimal containment approach, we quantify the asymmetry of convex bodies in $R^{n}$ with respect to reflections across affine subspaces of a given dimension. We pro…

math.FA2024

On the principal minors of Fourier matrices

Andrei Caragea, Dae Gwan Lee

For the $N$ -dimensional Fourier matrix $F_{N}$ , we prove that if $N \geq 4$ is square-free, then every $2 \times 2$ and $3 \times 3$ principal minor of $F_{N}$ is non…

math.CA2021★ 9 cited

A note on exponential Riesz bases

Andrei Caragea, Dae Gwan Lee

We prove that if $I_{ℓ} = [a_{ℓ}, b_{ℓ})$ , $ℓ = 1, \dots, L$ , are disjoint intervals in $[0, 1)$ with the property that the numbers $1, a_{1}, \dots, a_{L}, b_{1}, \dots, b_{L}$ are l…

math.FA2021

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…

math.FA2020★ 7 cited

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…

math.FA2019★ 1 cited

Time-Frequency Shift Invariance of Gabor Spaces with an $S_{0}$ -Generator

Andrei Caragea, Dae Gwan Lee, Friedrich Philipp +1

We consider Gabor Riesz sequences generated by a lattice $Λ \subset R^{2}$ and a window function $g \in L^{2} (R)$ which is well localized in both time and frequency. W…

math.FA2019

A quantitative subspace Balian-Low theorem

Andrei Caragea, Dae Gwan Lee, Friedrich Philipp +1

Let $G \subset L^{2} (R)$ be the subspace spanned by a Gabor Riesz sequence $(g, Λ)$ with $g \in L^{2} (R)$ and a lattice $Λ \subset R^{2}$ of rational density.…

math.FA2018

A Balian-Low Theorem for Subspaces

A. Caragea, D. Lee, G. E. Pfander +1

We extend the Balian-Low theorem to Gabor subspaces of $L^{2} (R)$ by involving the concept of additional time-frequency shift invariance. We prove that if a Gabor system on a…