We consider a class of linear Schrödinger 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.

Wave packet analysis of Schroedinger equations in analytic functions spaces / Elena, Cordero; Nicola, Fabio; Luigi, Rodino. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 278:(2015), pp. 182-209. [10.1016/j.aim.2015.03.014]

Wave packet analysis of Schroedinger equations in analytic functions spaces

NICOLA, FABIO;
2015

Abstract

We consider a class of linear Schrödinger 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.
File in questo prodotto:
File Dimensione Formato  
AIM2015-revised.pdf

Open Access dal 16/04/2017

Descrizione: Postprint
Tipologia: 2. Post-print / Author's Accepted Manuscript
Licenza: Creative commons
Dimensione 407.86 kB
Formato Adobe PDF
407.86 kB Adobe PDF Visualizza/Apri
AIM2015-editoriale.pdf

non disponibili

Descrizione: Postprint editoriale
Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 524.53 kB
Formato Adobe PDF
524.53 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2586754