Vol. 9, No. 3, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 7, 1539–1791
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
Cover
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
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|(k+p1)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
Mathematical Subject Classification 2010
Primary: 35B40
Milestones
Received: 22 March 2014
Revised: 24 November 2015
Accepted: 30 January 2016
Published: 17 June 2016
Authors
Hajer Bahouri
Université Paris Est
Laboratoire d’Analyse et de Mathématiques Appliquées, UMR CNRS 8050
61, avenue du Général de Gaulle
94010 Créteil Cedex
France
Clotilde Fermanian-Kammerer
Université Paris Est
Laboratoire d’Analyse et de Mathématiques Appliquées, UMR CNRS 8050
61, avenue du Général de Gaulle
94010 Créteil Cedex
France
Isabelle Gallagher
Institut de Mathématiques UMR 7586
Université Paris Diderot (Paris 7)
Bâtiment Sophie Germain, Case 7012
75205 Paris Cedex 13
France