Integral Representations for the Class of Generalized Metaplectic Operators View Full Text


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Article Info

DATE

2015-08

AUTHORS

Elena Cordero, Fabio Nicola, Luigi Rodino

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. More... »

PAGES

694-714

References to SciGraph publications

  • 2010-06. Boundedness of Schrödinger Type Propagators on Modulation Spaces in JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
  • 2014-09. On the Schrödinger equation with potential in modulation spaces in JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS
  • 2012-08. Approximation of Fourier Integral Operators by Gabor Multipliers in JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
  • 2001. Foundations of Time-Frequency Analysis in NONE
  • 2002-05. On the Integral Representations for Metaplectic Operators in JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
  • 2011. Symplectic Methods in Harmonic Analysis and in Mathematical Physics in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00041-014-9384-8

    DOI

    http://dx.doi.org/10.1007/s00041-014-9384-8

    DIMENSIONS

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