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Journal of Fourier Analysis and Applications

, Volume 16, Issue 2, pp 294–310 | Cite as

On the Wave Equation Associated to the Hermite and the Twisted Laplacian

  • Piero D’AnconaEmail author
  • Vittoria Pierfelice
  • Fulvio Ricci
Article

Abstract

The dispersive properties of the wave equation u tt +Au=0 are considered, where A is either the Hermite operator −Δ+|x|2 or the twisted Laplacian −( x iy)2/2−( y +ix)2/2. In both cases we prove optimal L 1L dispersive estimates. More generally, we give some partial results concerning the flows exp (itL ν ) associated to fractional powers of the twisted Laplacian for 0<ν<1.

Keywords

Wave equation Strichartz estimates Decay estimates Dispersive equations Schrödinger equation Harmonic analysis Almost periodicity 

Mathematics Subject Classification (2000)

35L05 35Q40 58J45 11K70 11L03 

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Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  • Piero D’Ancona
    • 1
    Email author
  • Vittoria Pierfelice
    • 2
  • Fulvio Ricci
    • 3
  1. 1.Dipartimento di MatematicaUnversità di Roma “La Sapienza”RomeItaly
  2. 2.Bâtiment de MatématiquesUnversité d’OrléansOrléans Cedex 2France
  3. 3.Classe di ScienzeScuola Normale SuperiorePisaItaly

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