Local Dispersive and Strichartz Estimates for the Schr?dinger Operator on the Heisenberg Group  

作　　者：Hajer Bahouri Isabelle Gallagher 

机构地区：[1]CNRS&Sorbonne Universite Laboratoire Jacques-Louis Lions(LJLL)UMR 75984,Place Jussieu 75005 Paris,France [2]DMA,Ecole Normale Superieure,CNRS,PSL Research University,75005 Paris,France [3]UFR de Mathematiques,Universitéde Paris,75013 Paris,France

出　　处：《Communications in Mathematical Research》2023年第1期1-35,共35页数学研究通讯（英文版）

摘　　要：It was proved by Bahouri et al.[9]that the Schrodinger equation on the Heisenberg group H^(d),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 H^(d) for the linear Schrodinger equation,by a refined study of the Schrodinger ker-nel St on H^(d).The sharpness of these estimates is discussed through several examples.Our approach,based on the explicit formula of the heat kernel on H^(d) derived by Gaveau[19],is achieved by combining complex analysis and Fourier-Heisenberg tools.As a by-product of our results we establish local Stri-chartz estimates and prove that the kernel St concentrates on quantized hori-zontal hyperplanes of H^(d).

关 键 词：Heisenberg group Schrodinger equation dispersive estimates Strichartz estimates 

分 类 号：O212.1[理学—概率论与数理统计]