Pré-Publication, Document De Travail Année : 2011

Schrödinger propagator and the Dunkl Laplacian

Résumé

We establish Strichartz estimates for a generalized Hermite--Schrödinger equation associated to a family of differential-difference operators involving the Dunkl Laplacian and unbounded potentials. This family includes the Hermite and Laguerre differential operators in particular. The study relies on the analysis of the so-called (k,a)-generalized semigroup studied by Ben Said-Kobayashi and Orsted. Moreover, we prove that homogeneous Strichartz estimates for the Schrödinger equation associated to the Dunkl Laplacian can be obtained from those for the generalized Hermite--Schrödinger equation.

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Dates et versions

hal-00578446 , version 1 (21-03-2011)
hal-00578446 , version 2 (03-03-2016)

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  • HAL Id : hal-00578446 , version 1

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Salem Ben Said, A.K. Nandakumaran, P.K. Ratnakumar. Schrödinger propagator and the Dunkl Laplacian. 2011. ⟨hal-00578446v1⟩
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