# 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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https://hal.archives-ouvertes.fr/hal-00466144
Contributor : Vittoria Pierfelice <>
Submitted on : Monday, March 22, 2010 - 5:38:07 PM
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### Citation

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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