Abstract
The present paper is dedicated to the proof of dispersive estimates on stratified Lie groups of step 2 for the linear Schrödinger equation involving a sublaplacian. It turns out that the propagator behaves like a wave operator on a space of the same dimension as the center of the group, and like a Schrödinger operator on a space of the same dimension as the radical of the canonical skew-symmetric form, which suggests a decay rate . We identify a property of the canonical skew-symmetric form under which we establish optimal dispersive estimates with this rate. The relevance of this property is discussed through several examples.
Citation
Hajer Bahouri. Clotilde Fermanian-Kammerer. Isabelle Gallagher. "Dispersive estimates for the Schrödinger operator on step-2 stratified Lie groups." Anal. PDE 9 (3) 545 - 574, 2016. https://doi.org/10.2140/apde.2016.9.545
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