4 papers
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…
On Modulation and Translation Invariant Operators and the Heisenberg Module
Arvin Lamando, Henry McNulty
We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered,…
Metaplectic Quantum Time--Frequency Analysis, Operator Reconstruction and Identification
Henry McNulty
The problem of identifying and reconstructing operators from a diagonal of the Gabor matrix is considered. The framework of Quantum Time--Frequency Analysis is used, wherein this p…