7 papers · 1 filter
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…
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…
Translation Invariant Operators on Polyanalytic Sobolev-Fock Spaces
Henry McNulty
We examine translation invariant operators on the Polyanalytic Sobolev-Fock spaces and show that they take the form \begin{align*} S_ϕ F(z) = \int_{\mathbb{C}^n} F(w)e^{πz\cdot \ov…
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,…
Quantum Time-Frequency Analysis and Pseudodifferential Operators
Franz Luef, Henry McNulty
We introduce Quantum Time-Frequency Analysis, which expands the approach of Quantum Harmonic Analysis to include modulations of operators in addition to translations. This is done…
Time-Frequency Analysis and Coorbit Spaces of Operators
Monika Dörfler, Franz Luef, Henry McNulty +1
We introduce an operator valued Short-Time Fourier Transform for certain classes of operators with operator windows, and show that the transform acts in an analogous way to the Sho…