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 −(∇_x − iy)^2/2 − (∇_y + ix)^2/2. In both cases we prove optimal L^1 − L^∞ 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.
On the wave equation associated to the Hermite and the twisted Laplacian
RICCI, Fulvio
2010
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 −(∇_x − iy)^2/2 − (∇_y + ix)^2/2. In both cases we prove optimal L^1 − L^∞ 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.File in questo prodotto:
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D'AnconaOn the wave equation associated to the Hermite and the twisted LaplacianJ Fourier Anal Appl2010294-31016.pdf
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