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On the wave equation associated to the Hermite and the twisted Laplacian

Abstract : The dispersive properties of the wave equation $u_{tt}+Au=0$ are considered, where $A$ is either the Hermite operator $-\Delta+|x|^{2}$ or the twisted Laplacian $-(\nabla_{x}-iy)^{2}/2-(\nabla_{y}+ix)^{2}/2$. In both cases we prove optimal $L^{1}-L^{\infty}$ dispersive estimates. More generally, we give some partial results concerning the flows $\exp(itL^{\nu})$ associated to fractional powers of the twisted Laplacian for $0<\nu<1$.
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Submitted on : Monday, March 22, 2010 - 5:38:07 PM
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Piero d'Ancona, Vittoria Pierfelice, Fulvio Ricci. On the wave equation associated to the Hermite and the twisted Laplacian. Journal of Fourier Analysis and Applications, Springer Verlag, 2010, 16 (2), pp.294-310. ⟨10.1007/s00041-009-9104-y⟩. ⟨hal-00466144⟩

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