Author： Mejjaoli Hatem
Publisher： Taylor & Francis Ltd
ISSN： 0003-6811
Source： Applicable Analysis, Vol.92, Iss.8, 2013-08, pp. : 1597-1626
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Abstract
We obtain dispersive estimates for the linear Dunkl-Schrödinger equations with and without quadratic potential. As a consequence, we prove the local well-posedness for semilinear Dunkl-Schrödinger equations with polynomial nonlinearity in certain magnetic field. Furthermore, we study many applications: as the uncertainty principles for the Dunkl transform via the Dunkl-Schrödinger semigroups, the embedding theorems for the Sobolev spaces associated with the generalized Hermite semigroup. Finally, almost every where convergence of the solutions of the Dunkl-Schrödinger equation is also considered.
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