Sparsity properties for phase-space representations of several types of operators have been extensively studied in recent articles, including pseudodifferential, Fourier integral and metaplectic operators, with applications to the analysis of Schrödinger-type evolution equations. It has been proved that such operators are approximately diagonalized by Gabor wave packets. While the latter are expected to undergo some spreading phenomenon, there is no record of this issue in the aforementioned results. In this note we prove refined estimates for the Gabor matrix of metaplectic operators, also of generalized type, where sparsity, spreading and dispersive properties are all noticeable. We provide applications to the propagation of singularities for the Schrödinger equation.

Dispersion, spreading and sparsity of Gabor wave packets for metaplectic and Schrödinger operators

Cordero E.;Nicola F.;Trapasso S. I.
2021-01-01

Abstract

Sparsity properties for phase-space representations of several types of operators have been extensively studied in recent articles, including pseudodifferential, Fourier integral and metaplectic operators, with applications to the analysis of Schrödinger-type evolution equations. It has been proved that such operators are approximately diagonalized by Gabor wave packets. While the latter are expected to undergo some spreading phenomenon, there is no record of this issue in the aforementioned results. In this note we prove refined estimates for the Gabor matrix of metaplectic operators, also of generalized type, where sparsity, spreading and dispersive properties are all noticeable. We provide applications to the propagation of singularities for the Schrödinger equation.
2021
55
405
425
https://arxiv.org/abs/2005.03911
Almost diagonalization; Dispersive estimates; Gabor wave packets; Metaplectic operators; Modulation spaces; Phase space analysis; Schrödinger equation; Wigner distribution
Cordero E.; Nicola F.; Trapasso S.I.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1837269
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