Wave packet analysis of Schrodinger equations in analytic function spaces

Abstract

We consider a class of linear Schroedinger equations in R^d, with analytic symbols. We prove a global-in-time integral representation for the corresponding propagator as a generalized Gabor multiplier with a window analytic and decaying exponentially at infinity, which is transported by the Hamiltonian flow. We then provide three applications of the above result: the exponential sparsity in phase space of the corresponding propagator with respect to Gabor wave packets, a wave packet characterization of Fourier integral operators with analytic phases and symbols, and the propagation of analytic singularities.

26 pages

References in corpus (3)

• Generalized Metaplectic Operators and the Schrödinger Equation with a Potential in the Sjöstrand Class
• Estimates on modulation spaces for Schrödinger evolution operators with quadratic and sub-quadratic potentials
• A remark on the ultra-analytic smoothing properties of the spatially homogeneous Landau equation

Cited by in corpus (6)

• Propagation of singularities for semilinear Schrödinger equations
• Boundedness of Pseudodifferential Operators with symbols in Wiener amalgam spaces on Modulation Spaces
• Modulation spaces associated to tensor products of amalgam spaces
• Invertibility of matrix type operators of infinite order with exponential off-diagonal decay
• Convergence in $L^p$ for Feynman path integrals
• Anisotropic Shubin operators and eigenfunctions expansions in Gelfand-Shilov spaces