Stability of Gabor frames under small time Hamiltonian evolutions

Abstract

We consider Hamiltonian deformations of Gabor systems, where the window evolves according to the action of a Schrödinger propagator and the phase-space nodes evolve according to the corresponding Hamiltonian flow. We prove the stability of the frame property for small times and Hamiltonians consisting of a quadratic polynomial plus a potential in the Sjöstrand class with bounded second order derivatives. This answers a question raised in [de Gosson, M. Symplectic and Hamiltonian Deformations of Gabor Frames. Appl. Comput. Harmon. Anal. Vol. 38 No.2, (2015) p.196--221.]

11 pages. Minor revision

References in corpus (4)

• Generalized Metaplectic Operators and the Schrödinger Equation with a Potential in the Sjöstrand Class
• Deformation of Gabor systems
• The $abc$-problem for Gabor systems
• Symplectic and Hamiltonian Deformations of Gabor Frames

Cited by in corpus (6)

• Almost diagonalization of $\tau$-pseudodifferential operators with symbols in Wiener amalgam and modulation spaces
• A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators
• Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
• Almost Diagonalization of Pseudodifferential Operators
• Discrete Vector-Valued Nonuniform Gabor Frames
• Deforming the Window of a Gabor Frame: the Ellipsoid Method