Publications
Journal Articles
2.
Cordero, Elena; Giacchi, Gianluca; Pucci, Edoardo; Trapasso, S. Ivan
Sparse Gabor representations of metaplectic operators: controlled exponential decay and Schrödinger confinement Journal Article
In: Adv. Math., vol. 490, pp. 110828, 2026.
Abstract | Links | BibTeX | Tags: Gabor analysis, mathematical physics, metaplectic operators, Schrödinger equations, time-frequency analysis
@article{CGPT_25,
title = {Sparse Gabor representations of metaplectic operators: controlled exponential decay and Schrödinger confinement},
author = {Elena Cordero and Gianluca Giacchi and Edoardo Pucci and S. Ivan Trapasso},
url = {https://arxiv.org/abs/2508.02226, arXiv
https://www.sciencedirect.com/science/article/pii/S0001870826000502/pdfft?md5=7ed5c060ac7fbd7b68081d585554055a&pid=1-s2.0-S0001870826000502-main.pdf, PDF},
doi = {10.1016/j.aim.2026.110828},
year = {2026},
date = {2026-02-02},
urldate = {2026-02-02},
journal = {Adv. Math.},
volume = {490},
pages = {110828},
abstract = {Motivated by the phase space analysis of Schrödinger evolution operators, in this paper we investigate how metaplectic operators are approximately diagonalized along the corresponding symplectic flows by exponentially localized Gabor wave packets. Quantitative bounds for the matrix coefficients arising in the Gabor wave packet decomposition of such operators are established, revealing precise exponential decay rates together with subtler dispersive and spreading phenomena. To this aim, we present several novel results concerning the time-frequency analysis of functions with controlled Gelfand-Shilov regularity, which are of independent interest. As a byproduct, we generalize Vemuri's Gaussian confinement results for the solutions of the quantum harmonic oscillator in two respects, namely by encompassing general exponential decay rates as well as arbitrary quadratic Schrödinger propagators. In particular, we extensively discuss some prominent models such as the harmonic oscillator, the free particle in a constant magnetic field and fractional Fourier transforms.},
keywords = {Gabor analysis, mathematical physics, metaplectic operators, Schrödinger equations, time-frequency analysis},
pubstate = {published},
tppubtype = {article}
}
Motivated by the phase space analysis of Schrödinger evolution operators, in this paper we investigate how metaplectic operators are approximately diagonalized along the corresponding symplectic flows by exponentially localized Gabor wave packets. Quantitative bounds for the matrix coefficients arising in the Gabor wave packet decomposition of such operators are established, revealing precise exponential decay rates together with subtler dispersive and spreading phenomena. To this aim, we present several novel results concerning the time-frequency analysis of functions with controlled Gelfand-Shilov regularity, which are of independent interest. As a byproduct, we generalize Vemuri’s Gaussian confinement results for the solutions of the quantum harmonic oscillator in two respects, namely by encompassing general exponential decay rates as well as arbitrary quadratic Schrödinger propagators. In particular, we extensively discuss some prominent models such as the harmonic oscillator, the free particle in a constant magnetic field and fractional Fourier transforms.
1.
Cordero, Elena; Nicola, Fabio; Trapasso, S. Ivan
Dispersion, spreading and sparsity of Gabor wave packets for metaplectic and Schrödinger operators Journal Article
In: Appl. Comput. Harmon. Anal., vol. 55, pp. 405–425, 2021.
Abstract | Links | BibTeX | Tags: Gabor analysis, mathematical physics, metaplectic operators, Schrödinger equations, time-frequency analysis
@article{CNT_ACHA_21,
title = {Dispersion, spreading and sparsity of Gabor wave packets for metaplectic and Schrödinger operators},
author = {Elena Cordero and Fabio Nicola and S. Ivan Trapasso},
url = {https://arxiv.org/abs/2005.03911, arXiv},
doi = {10.1016/j.acha.2021.06.007},
year = {2021},
date = {2021-11-30},
urldate = {2021-11-30},
journal = {Appl. Comput. Harmon. Anal.},
volume = {55},
pages = {405–425},
publisher = {Academic Press},
abstract = {Sparsity properties for phase-space representations of several types of operators have been extensively studied in recent papers, including pseudodifferential, Fourier integral and metaplectic operators, with applications to time-frequency 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 paper 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.},
keywords = {Gabor analysis, mathematical physics, metaplectic operators, Schrödinger equations, time-frequency analysis},
pubstate = {published},
tppubtype = {article}
}
Sparsity properties for phase-space representations of several types of operators have been extensively studied in recent papers, including pseudodifferential, Fourier integral and metaplectic operators, with applications to time-frequency 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 paper 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.