32 citations · 193 across the 48 of their papers we have counts for
5 papers · 1 filter
Spectral and regularity properties of an operator calculus related to Landau quantization
Maurice de Gosson, Franz Luef
The theme of this work is that the theory of charged particles in a uniform magnetic field can be generalized to a large class of operators if one uses an extended a class of Weyl…
Quantum theta functions and Gabor frames for modulation spaces
Franz Luef, Yuri I. Manin
Representations of the celebrated Heisenberg commutation relations in quantum mechanics and their exponentiated versions form the starting point for a number of basic constructions…
A new approach to the star-genvalue equation
M. de Gosson, Franz Luef
We show that the eigenvalues and eigenfunctions of the stargenvalue equation can be completely expressed in terms of the corresponding eigenvalue problem for the quantum Hamiltonia…
Projective modules over noncommutative tori are multi-window Gabor frames for modulation spaces
Franz Luef
In the present investigation we are linking noncommutative geometry over noncommutative tori with Gabor analysis, where the first has its roots in operator algebras and the second…
The Multi-Dimensional Hardy Uncertainty Principle and its Interpretation in Terms of the Wigner Distribution; Relation With the Notion of Symplectic Capacity
Maurice de Gosson, Franz Luef
We extend Hardy's uncertainty principle for a square integrable function and its Fourier transform to the multidimensional case using a symplectic diagonalization. We use this exte…