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Article Dans Une Revue Analysis & PDE Année : 2016

DISPERSIVE ESTIMATES FOR THE SCHRODINGER OPERATOR ON STEP 2 STRATIFIED LIE GROUPS

Résumé

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 p as the center of the group, and like a Schrödinger operator on a space of the same dimension k as the radical of the canonical skew-symmetric form, which suggests a decay rate of exponant -(k+p-1)/2. In this article, 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.
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Dates et versions

hal-00963846 , version 1 (25-03-2014)
hal-00963846 , version 2 (03-04-2015)

Identifiants

  • HAL Id : hal-00963846 , version 2

Citer

Hajer Bahouri, Clotilde Fermanian Kammerer, Isabelle Gallagher. DISPERSIVE ESTIMATES FOR THE SCHRODINGER OPERATOR ON STEP 2 STRATIFIED LIE GROUPS. Analysis & PDE, 2016, 9 (3). ⟨hal-00963846v2⟩
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