Local dispersive and Strichartz estimates for the Schrödinger operator on the Heisenberg group - Laboratoire Jacques-Louis Lions
Journal Articles Communications in Mathematical Research Year : 2023

Local dispersive and Strichartz estimates for the Schrödinger operator on the Heisenberg group

Abstract

It was proved by Bahouri et al. [9] that the Schrödinger equation on the Heisenberg group Hd, involving the sublaplacian, is an example of a totally non-dispersive evolution equation: for this reason global dispersive estimates cannot hold. This paper aims at establishing local dispersive estimates on Hd for the linear Schrödinger equation, by a refined study of the Schrödinger kernel St on Hd. The sharpness of these estimates is discussed through several examples. Our approach, based on the explicit formula of the heat kernel on Hd derived by Gaveau [19], is achieved by combining complex analysis and Fourier-Heisenberg tools. As a by-product of our results we establish local Strichartz estimates and prove that the kernel St concentrates on quantized horizontal hyperplanes of Hd.
Fichier principal
Vignette du fichier
Kernel_final.pdf (529.34 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04744901 , version 1 (19-10-2024)

Identifiers

Cite

Hajer Bahouri, Isabelle Gallagher. Local dispersive and Strichartz estimates for the Schrödinger operator on the Heisenberg group. Communications in Mathematical Research, 2023, 39 (1), ⟨10.4208/cmr.2021-0101⟩. ⟨hal-04744901⟩
0 View
0 Download

Altmetric

Share

More