Introduction to QHA and Gabor frames

Franz Luef (NTNU, Trondheim)

May 05. 2025, 09:30 — 10:30

We present the key notions of quantum harmonic analysis (QHA) such as the operator convolutions and the Fourier-Wigner transform, with a focus on their interpretation in terms of time-frequency analysis such as the short-time Fourier transform, localization operators and the spreading function. The interaction between QHA and time-frequency analysis has led to the introduction of the notions of mixed-state localization operators, the Cohen's class of an operator and the operator short-time Fourier transform. 
Gabor frames come naturally up when looking for a reconstruction formula for functions in terms of sampled values of the short-time Fourier transform and after discussing their basic properties we also link it to QHA, and that the Janssen representation of the Gabor frame operator is a special case of a Poisson summation formula for an operator and its Fourier-Wigner transform. We close with a natural extension of Gabor frames from the perspective of QHA, namely Gabor g-frames.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Quantum Harmonic Analysis (Workshop)
Organizer(s):
Markus Faulhuber (U of Vienna)
Hans G. Feichtinger (U of Vienna)
Franz Luef (NTNU, Trondheim)