#### Vol. 9, No. 3, 2016

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
Dispersive estimates for the Schrödinger operator on step-2 stratified Lie groups

### Hajer Bahouri, Clotilde Fermanian-Kammerer and Isabelle Gallagher

Vol. 9 (2016), No. 3, 545–574
##### 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 $p$ 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 $|t{|}^{-\left(k+p-1\right)∕2}$. 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.

##### Keywords
step-2 stratified Lie groups, Schrödinger equation, dispersive estimates, sublaplacian
Primary: 35B40