CINECA IRIS Institutional Research Information System
IRIS è il sistema di gestione integrata dei dati della ricerca (persone, progetti, pubblicazioni, attività) adottato dall'Università degli Studi di Torino.
AperTO è l'archivio istituzionale Open Access destinato a raccogliere, rendere visibile e conservare la produzione scientifica dell'Università degli Studi di Torino.
EnglishRecent papers show how tight frames of curvelets and shearlets provide optimally sparse representation of hyperbolic-type Fourier Integral Operators (FIOs). In this paper we address to another class of FIOs, employed by Helffer and Robert to study spectral properties of globally elliptic operators of Quantum Mechanics, and hence studied by many other authors. An example is provided by the resolvent of the Cauchy problem for the Schrödinger equation with a quadratic Hamiltonian. We show that Gabor frames provide optimally sparse representations of such operators. Numerical examples for the Schrödinger case demonstrate the fast computation of these operators.
| Titolo: | Sparsity of Gabor representation of Schrödinger propagators |
| Autori Riconosciuti: | |
| Autori: | E. Cordero; F. Nicola; L. Rodino |
| Data di pubblicazione: | 2009 |
| Abstract: | Recent papers show how tight frames of curvelets and shearlets provide optimally sparse representation of hyperbolic-type Fourier Integral Operators (FIOs). In this paper we address to another class of FIOs, employed by Helffer and Robert to study spectral properties of globally elliptic operators of Quantum Mechanics, and hence studied by many other authors. An example is provided by the resolvent of the Cauchy problem for the Schrödinger equation with a quadratic Hamiltonian. We show that Gabor frames provide optimally sparse representations of such operators. Numerical examples for the Schrödinger case demonstrate the fast computation of these operators. |
| Volume: | 26 |
| Fascicolo: | 3 |
| Pagina iniziale: | 357 |
| Pagina finale: | 370 |
| Digital Object Identifier (DOI): | 10.1016/j.acha.2008.08.003 |
| Parole Chiave: | Fourier integral operators; Gabor frames; Modulation spaces; Schrödinger equation; Short-time Fourier transform |
| Rivista: | APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS |
| Appare nelle tipologie: | 03A-Articolo su Rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| sparsity.pdf | 1 Ver. finale autore | Accesso riservato | Utenti riconosciuti Richiedi una copia |
http://hdl.handle.net/2318/46381
Copyright © 2019