Quantum Harmonic Analysis
This workshop intends to deepen existing connections and establish new ones between quantum harmonic analysis, the theory of Toeplitz operators on Bargmann-Fock spaces and Bergman spaces, mathematical physics, quantum information, machine learning, and time-frequency analysis.
Background summary:
Quantum harmonic analysis emerged from the article Quantum harmonic analysis in phase space, J. Math. Phys., 25(5):1404–1411, 1984 by R. F. Werner. The theory is based on the key insight that the analogs of Wiener’s approximation theorem for L-p spaces hold for certain operators (Schatten class operators). For the theory to work, the following extensions of classical concepts for functions are needed:
(1) Banach spaces for operators
(2) A translation for operators
(3) A convolution for operators
(4) A Fourier transform for operators
These concepts shall be re-called in introductory lectures.
The workshop acknowledges additional support from Österreichische Forschungsgemeinschaft (oefg.at)
and the Austrian Science Fund (FWF) (fwf.ac.at)
May 5, 2025
May 6, 2025
May 7, 2025
May 8, 2025
May 9, 2025
09:00 — 09:30
Registration & Welcome
09:30 — 10:30
Franz Luef (NTNU, Trondheim)
Introduction to QHA and Gabor frames
Introduction to QHA and Gabor frames
10:30 — 11:15
Coffee Break
11:15 — 12:00
Hans G. Feichtinger (U of Vienna)
Discrete Time-Frequency Analysis via MATLAB
Discrete Time-Frequency Analysis via MATLAB
12:00 — 14:00
Lunch Break & Registration
14:00 — 14:30
Michael Speckbacher (Acoustics Research Institute, Vienna)
Spectral deviation of Toeplitz operators on vector-valued reproducing kernel Hilbert spaces
Spectral deviation of Toeplitz operators on vector-valued reproducing kernel Hilbert spaces
14:30 — 15:00
Erling Svela (NTNU, Trondheim)
A large sieve principle for the operator STFT with applications to Cohen's class
A large sieve principle for the operator STFT with applications to Cohen's class
15:00 — 15:15
Coffee Break
15:15 — 16:15
Luis Daniel Abreu (U of Vienna)
Classical phase space representations of density operators with classical and quantum Gabor transforms
Classical phase space representations of density operators with classical and quantum Gabor transforms
16:15 — 16:45
Are Austad (U Oslo)
New classes of hermitian algebras
New classes of hermitian algebras
09:30 — 10:30
Elena Cordero (U Torino)
Wigner Analysis of Operators controlling ghost frequencies
Wigner Analysis of Operators controlling ghost frequencies
10:30 — 11:00
Coffee Break
11:00 — 11:30
Edoardo Pucci (U Torino)
Understanding of linear operators through Wigner analysis
Understanding of linear operators through Wigner analysis
11:30 — 12:00
Helge Jørgen Samuelsen (NTNU, Trondheim)
Fourier-Wigner multipliers in Quantum Harmonic Analysis
Fourier-Wigner multipliers in Quantum Harmonic Analysis
12:00 — 14:00
Lunch Break
14:00 — 15:00
Robert Fulsche (Leibniz U Hannover)
Heisenberg-smooth operators and QHA
Heisenberg-smooth operators and QHA
15:00 — 15:15
Coffee Break
15:15 — 15:45
Michael Gjertsen (NTNU, Trondheim)
Towards a Theory of Quantum Harmonic Analysis on Riemannian Manifolds
Towards a Theory of Quantum Harmonic Analysis on Riemannian Manifolds
15:45 — 16:15
Joachim Toft (Linnaeus U)
Orlicz convolutions in QHA with applications to Orlicz Schatten properties for Toeplitz operators
Orlicz convolutions in QHA with applications to Orlicz Schatten properties for Toeplitz operators
16:15 — 16:45
Azita Mayeli (CUNY, New York)
Localization operators, wave packets, and eigenvalue distributions
Localization operators, wave packets, and eigenvalue distributions
09:30 — 10:30
Richard Küng (JKU, Linz)
Provably efficient machine learning for quantum many-body problems
Provably efficient machine learning for quantum many-body problems
10:30 — 11:00
Coffee Break
11:00 — 11:30
Mario Ullrich (JKU, Linz)
How many measurements are needed to learn a vector?
How many measurements are needed to learn a vector?
11:30 — 12:00
Ahmed Abdeljawad (RICAM, Linz)
Approximation with Neural Networks in Fourier Lebesgue Spaces
Approximation with Neural Networks in Fourier Lebesgue Spaces
12:00 — 14:00
Lunch Break
14:00 — 15:00
David Gross (U Cologne)
On Euler or on Cayley
On Euler or on Cayley
15:00 — 15:15
Coffee Break
15:15 — 15:45
Jean Pierre Gazeau (Paris Cité U)
Gabor regularisation of Minkowski space-time
Gabor regularisation of Minkowski space-time
15:45 — 16:15
Apostolos Vourdas (U of Bradford)
The Grothendieck inequality in Quantum Mechanics and Harmonic Analysis
The Grothendieck inequality in Quantum Mechanics and Harmonic Analysis
16:15 — 16:45
Mariano del Olmo (UVS)
Special functions, Groups, Harmonic Analysis and Rigged Hilbert Spaces
Special functions, Groups, Harmonic Analysis and Rigged Hilbert Spaces
16:45 — 18:30
Discussion Time
at the Common Room
18:30
Social Event
09:30 — 10:00
Margit Pap (U Pécs)
Properties of hyperbolic convolution on the unit disc and applications
Properties of hyperbolic convolution on the unit disc and applications
10:00 — 10:30
Carlos Cabrelli (U of Buenos Aires)
Frames by orbits of Bounded Operators
Frames by orbits of Bounded Operators
10:30 — 11:00
Coffee Break
11:00 — 12:00
Ursula Molter (U of Buenos Aires)
Weaving Frames and Riesz bases
Weaving Frames and Riesz bases
12:00 — 14:00
Lunch Break
14:00 — 14:30
Vishwa Dewage (Clemson U)
An operator heat semigroup and the Berger-Coburn theorem
An operator heat semigroup and the Berger-Coburn theorem
14:30 — 15:00
Johannes Testorf (NTNU, Trondheim)
Toeplitz and time-frequency localization operators on the flat torus
Toeplitz and time-frequency localization operators on the flat torus
15:00 — 15:15
Coffee Break
15:15 — 15:45
Raffael Hagger (Christian-Albrechts-U, Kiel)
Compact operators on locally compact abelian groups
Compact operators on locally compact abelian groups
15:45 — 16:15
Lukas Köhldorfer (Acoustics Research Institute, Vienna)
Approximation properties and characterization of operator coorbit spaces
Approximation properties and characterization of operator coorbit spaces
16:15 — 16:45
Hannes Wendt (U Oslo)
A Duflo-Moore theorem for ergodic group actions on semifinite von Neumann algebras
A Duflo-Moore theorem for ergodic group actions on semifinite von Neumann algebras
09:30 — 10:30
Irina Shafkulovska (U of Vienna)
Uncertainty Principles for Metaplectic Time-Frequency Representations
Uncertainty Principles for Metaplectic Time-Frequency Representations
10:30 — 10:45
Coffee Break
10:45 — 11:15
Gianluca Giacchi (U Svizzera Italiana)
Recent developments on Hardy's uncertainty principle
Recent developments on Hardy's uncertainty principle
11:15 — 11:45
Lenny Neyt (U of Vienna)
Hermite expansions for spaces of functions with nearly optimal time-frequency decay
Hermite expansions for spaces of functions with nearly optimal time-frequency decay
11:45 — 12:00
Short Break
12:00 — 12:30
Maurice de Gosson (Acoustics Research Institute, Vienna)
Polar Duality and the Donoho--Stark Uncertainty Principle
Polar Duality and the Donoho--Stark Uncertainty Principle
12:30
Lunch & End of Thematic Programme
Discussion Time & Coffee
Organizers
| Name | Affiliation |
|---|---|
| Markus Faulhuber | University of Vienna |
| Hans G. Feichtinger | University of Vienna |
| Franz Luef | Norwegian University for Science and Technology |
Attendees
| Name | Affiliation |
|---|---|
| Ahmed Abdeljawad | Radon Institute, RICAM |
| Luis Daniel Abreu | University of Vienna |
| Are Austad | University of Oslo |
| Aksel Bergfeldt | Ecole Normale Superieure |
| Carlos Cabrelli | University of Buenos Aires |
| Elena Cordero | University of Torino |
| Maurice de Gosson | Acoustics Research Institute |
| Mariano del Olmo | Universidad de Valladolid |
| Vishwa Dewage | Clemson University |
| Monika Dörfler | University of Vienna |
| Ulrik Enstad | University of Oslo |
| Robert Fulsche | Leibniz University Hannover |
| Jean Pierre Gazeau | Paris Cité University |
| Gianluca Giacchi | Università della Svizzera Italiana |
| Michael Gjertsen | Norwegian University for Science and Technology |
| Karlheinz Gröchenig | University of Vienna |
| David Gross | University of Cologne |
| Anupam Gumber | University of Vienna |
| Raffael Hagger | Christian-Albrechts-Universität zu Kiel |
| Jukka Kiukas | Aberystwyth University |
| Lukas Köhldorfer | Acoustics Research Institute |
| Richard Küng | Johannes Kepler Universität |
| Azita Mayeli | City University of New York |
| Henry McNulty | Cognite AS |
| Ursula Molter | University of Buenos Aires |
| Ryo Muramatsu | Tokyo University of Science |
| Lenny Neyt | University of Vienna |
| Eduard Ortega | Norwegian University for Science and Technology |
| Margit Pap | University of Pécs |
| Edoardo Pucci | University of Torino |
| Helge Jørgen Samuelsen | Norwegian University for Science and Technology |
| Norbert Schuch | University of Vienna |
| Irina Shafkulovska | University of Vienna |
| Mitra Shamsabadi | University of Vienna |
| Michael Speckbacher | Acoustics Research Institute |
| Erling Svela | Norwegian University for Science and Technology |
| Johannes Testorf | Norwegian University for Science and Technology |
| Joachim Toft | Linnaeus University |
| Alice Barbara Tumpach | Wolfgang Pauli Institut |
| Mario Ullrich | Johannes Kepler Universität |
| Apostolos Vourdas | University of Bradford |
| Hannes Wendt | University of Oslo |
At a glance
- Type:
- Workshop
- When:
- May 5, 2025 — May 9, 2025
- Where:
- ESI Boltzmann Lecture Hall
- Organizer(s):
-
Markus Faulhuber (U of Vienna)
Hans G. Feichtinger (U of Vienna)
Franz Luef (NTNU, Trondheim)