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

作     者：Hajer Bahouri Isabelle Gallagher Hajer Bahouri;Isabelle Gallagher

作者机构：CNRS&Sorbonne Universite Laboratoire Jacques-Louis Lions(LJLL)UMR 75984Place Jussieu 75005 ParisFrance DMAEcole Normale SuperieureCNRSPSL Research University75005 ParisFrance UFR de MathematiquesUniversitéde Paris75013 ParisFrance 

出 版 物：《Communications in Mathematical Research》 (数学研究通讯（英文版）)

年 卷 期：2023年第39卷第1期

页      面：1-35页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

主　　题：Heisenberg group Schrodinger equation dispersive estimates Strichartz estimates 

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 *** 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 *** 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 *** 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).