Limiting absorption principle for discrete Schr{ö}dinger operators with a Wigner-von Neumann potential and a slowly decaying potential

The limiting absorption principle for the discrete Wigner-von Neumann operator

We apply weighted Mourre commutator theory to prove the limiting absorption principle for the discrete Schr{ö}dinger operator perturbed by the sum of a Wigner-von Neumann and long-range type potential. In particular, this implies a new result concerning the absolutely continuous spectrum for these operators even for the one-dimensional operator. We show that methods of classical Mourre theory based on differential inequalities and on the generator of dilation cannot apply to the mentionned Schr{ö}dinger operators.

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…

A differential approach to the multi-marginal Schr{ö}dinger system

We develop an elementary and self-contained differential approach, in an $L^\infty$ setting, for well-posedness (existence, uniqueness and smooth dependence with respect to the data) for the multi-marginal Schr{ö}dinger system which arises in the entropic regularization of optimal transport problems.

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。

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].