11 papers
Harmoniq: Efficient Data Augmentation on a Quantum Computer Inspired by Harmonic Analysis
Kristina Kirova, Monika Doerfler, Franz Luef +1
Quantum machine learning has attracted significant interest in recent years. Most existing approaches, however, are variational in nature and require extensive parameter optimizati…
Bessel duality of Gabor systems: A von Neumann algebraic perspective
Ulrik Enstad, Franz Luef
Bessel duality of regular Gabor systems states that a Gabor system over a lattice is a Bessel sequence if and only if the corresponding Gabor system over the adjoint lattice is a B…
Quantum Harmonic Analysis and the Structure in Data: Augmentation
Monika Doerfler, Franz Luef, Henry McNulty
In this short note, we study the impact of data augmentation on the smoothness of principal components of high-dimensional datasets. Using tools from quantum harmonic analysis, we…
Approximation properties of operator coorbit spaces and sparsity classes
Monika Dörfler, Lukas Köhldorfer, Franz Luef +1
Extensions of coorbit spaces for functions to operators have been introduced by two different groups in \cite{doelumcskr24} and \cite{köbaLOC25}, where one is based on the coorbit…
Wiener's Tauberian theorem in classical and quantum harmonic analysis
Robert Fulsche, Franz Luef, Reinhard F. Werner
We investigate Wiener's Tauberian theorem from the perspective of limit functions, which results in several new versions of the Tauberian theorem. Based on this, we formulate and p…
On the transcendentality condition for Gaussian Gabor frames and Hermite super/multiwindow frames
Franz Luef, Johannes Testorf, Xu Wang
We give a criterion for higher-dimensional Gaussian Gabor frames, which is a reformulation of one of the main results in in a previous article by the first and last authors in more…