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Dispersive estimates
for the Schrödinger operator on step-2 stratified Lie
groups
Hajer Bahouri, Clotilde Fermanian-Kammerer and Isabelle Gallagher |
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Vol. 9 (2016), No. 3, 545–574
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Abstract |
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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. |
Keywords
step-2 stratified Lie groups, Schrödinger equation,
dispersive estimates, sublaplacian
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Mathematical Subject Classification 2010
Primary: 35B40
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Milestones
Received: 22 March 2014
Revised: 24 November 2015
Accepted: 30 January 2016
Published: 17 June 2016
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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 |
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| 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 |
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| Isabelle Gallagher | |
| Institut de Mathématiques UMR
7586 Université Paris Diderot (Paris 7) Bâtiment Sophie Germain, Case 7012 75205 Paris Cedex 13 France |
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