This article gives explicit integral formulas for the so-called generalized metaplectic operators, i.e. Fourier integral operators of Schrödinger type, having a symplectic matrix as their canonical transformation. These integrals are over specific linear subspaces of Rd , related to the d × d upper left-hand side submatrix of the underlying 2d×2d symplectic matrix. The arguments use the integral representations for the classical metaplectic operators obtained by Morsche and Oonincx in a previous paper, algebraic properties of symplectic matrices and time-frequency tools. As an application, we give a specific integral representation for solutions of the Cauchy problem of Schrödinger equations with bounded perturbations for every instant time t ∈ R, even at the (so-called) caustic points.

Integral Representations for the Class of Generalized Metaplectic Operators

CORDERO, Elena;RODINO, Luigi Giacomo
2015-01-01

Abstract

This article gives explicit integral formulas for the so-called generalized metaplectic operators, i.e. Fourier integral operators of Schrödinger type, having a symplectic matrix as their canonical transformation. These integrals are over specific linear subspaces of Rd , related to the d × d upper left-hand side submatrix of the underlying 2d×2d symplectic matrix. The arguments use the integral representations for the classical metaplectic operators obtained by Morsche and Oonincx in a previous paper, algebraic properties of symplectic matrices and time-frequency tools. As an application, we give a specific integral representation for solutions of the Cauchy problem of Schrödinger equations with bounded perturbations for every instant time t ∈ R, even at the (so-called) caustic points.
2015
21
4
694
714
http://arxiv.org/abs/1407.0841
Fourier Integral Operators; Metaplectic operators; Modulation spaces; Wigner distribution; Short-time Fourier transform; Schrödinger equation
E. Cordero; F. Nicola; L. Rodino
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/2318/1507853
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 11
social impact