Analysis & PDE

  • Anal. PDE
  • Volume 9, Number 3 (2016), 545-574.

Dispersive estimates for the Schrödinger operator on step-2 stratified Lie groups

Hajer Bahouri, Clotilde Fermanian-Kammerer, and Isabelle Gallagher

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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.

Article information

Source
Anal. PDE, Volume 9, Number 3 (2016), 545-574.

Dates
Received: 22 March 2014
Revised: 24 November 2015
Accepted: 30 January 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1510843261

Digital Object Identifier
doi:10.2140/apde.2016.9.545

Mathematical Reviews number (MathSciNet)
MR3518529

Zentralblatt MATH identifier
06600505

Subjects
Primary: 35B40: Asymptotic behavior of solutions

Keywords
step-2 stratified Lie groups Schrödinger equation dispersive estimates sublaplacian

Citation

Bahouri, Hajer; Fermanian-Kammerer, Clotilde; Gallagher, Isabelle. Dispersive estimates for the Schrödinger operator on step-2 stratified Lie groups. Anal. PDE 9 (2016), no. 3, 545--574. doi:10.2140/apde.2016.9.545. https://projecteuclid.org/euclid.apde/1510843261


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