Lower bounds for estimates of the Schrödinger maximal function

Schrödinger方程解的相位恢复

Phase retrieval for solutions of the Schr{ö}dinger equations

本文提出Schrödinger方程相位恢复的若干问题，给出部分解答及启发式思考。

On unique continuation for solutions of the Schr{ö}dinger equation on trees

We prove that if a solution of the time-dependent Schr{ö}dinger equation on an homogeneous tree with bounded potential decays fast at two distinct times then the solution is trivial. For the free Schr{ö}dinger operator, we use the spectral theory of the Laplacian and complex analysis and obtain a characterization of the initial conditions that lead to a sharp decay at any time. We then use the recent spectral decomposition of the Schr{ö}dinger operator with compactly supported potential due to Colin de Verdi{è}rre and Turc to extend our results in the presence of such potentials. Finally, we u…

标准N-球面和双曲N-空间上非线性Schr $\bf{\ddot{O}}$ dinger方程解的爆破

Blow-up of solutions to the nonlinear Schr$\bf{\ddot{O}}$dinger equations on standard N-sphere and hyperbolic N-space

本文部分解决了标准2-球面$S^2$和双曲2-空间$H^{2}(-1)$上的非线性Schr $\ddot{o}$ dinger方程有限时间爆破性质的长期未解决问题.利用类似的思想，我们在高维标准球面和双曲$n$ -空间上建立了这样的爆破结果。给出了具有$n\geq 2$的$n$维黎曼曲积流形的推广.

关于某些周期图上离散 Schrödinger 算子的三球不等式

On the Three Balls Inequality for Discrete Schr{ö}dinger Operators on Certain Periodic Graphs

本文利用 Carleman 估计研究周期图上离散磁性 Schrödinger 算子的定量唯一延拓，并将三球不等式推广至包含六角晶格的周期图族。

An uncertainty principle for solutions of the Schr{ö}dinger equation on H-type groups

In this paper we consider uncertainty principles for solutions of certain PDEs on H-type groups. We first prove that, contrary to the euclidean setting, the heat kernel on H-type groups is not characterized as the only solution of the heat equation that has sharp decay at 2 different times. We then prove the analogue of Hardy's Uncertainty Principle for solutions of the Schr{ö}dinger equation with potential on H-type groups. This extends the free case considered by Ben Saïd, Dogga and Thangavelu [BTD] and by Ludwig and M{ü}ller [LM].