9 papers
Endpoint Mapping Properties of Wave Operators for Schrödinger Operators in Dimensions
Han Cheng, Changxing Miao, Xiaohua Yao
We study endpoint mapping properties of low-energy wave operators for Schrödinger operators on , . In dimension four, we prove that a zero-energy reson…
Endpoint Mapping Properties of Wave Operators for Two-Dimensional Schrödinger Operators
Han Cheng, Changxing Miao, Xiaohua Yao
We establish sharp endpoint mapping properties for the wave operators of two-dimensional Schrödinger operators with real-valued decaying potentials . Toge…
Decay estimates for the two-dimensional Beam equation with potentials
Shuangshuang Chen, Han Cheng, Zijun Wan +1
This paper establishes time decay estimates for the following two-dimensional beam (plate) equation with a decaying real-valued potential : \begin{equation*} \partial_t^2 u + (Δ…
The boundedness of wave operators for the Laplace operator with finite rank perturbations
Han Cheng, Shanlin Huang, Avy Soffer +1
This paper investigates the boundedness of wave operators for the Laplace operator with finite rank perturbations \begin{equation*} H=-Δ+\sum\limits_{i=1}^N\langle\cdot\,, φ_…
The -boundedness of wave operators for higher order Schrödinger operator with zero singularities in low odd dimensions
Han Cheng, Avy Soffer, Zhao Wu +1
This paper investigates the -bounds of wave operators for higher-order Schrödinger operators on , with and real-valued decaying potent…
Pointwise estimates for the fundamental solutions of higher order schrödinger equations with finite rank perturbations
Xinyi Chen, Han Cheng, Shanlin Huang
This paper is dedicated to studying pointwise estimates of the fundamental solution for the higher order Schrödinger equation: % we investigate the fundamental solution of the high…
Pointwise estimates for the fundamental solutions of higher order Schrödinger equations in odd dimensions II: high dimensional case
Han Cheng, Shanlin Huang, Tianxiao Huang +1
In this paper, for any odd and any integer with , we study the fundamental solution of the higher order Schrödinger equation \begin{equation*} \mathrm{i}\partial…
Pointwise estimates for the fundamental solutions of higher order Schrödinger equations in low odd dimensions
Han Cheng, Shanlin Huang, Tianxiao Huang +1
In this paper, we study the fundamental solution of the higher order Schrödinger equation \begin{equation*} \mathrm{i}\partial_t u(x,t) = \big((-Δ)^m + V(x)\big)u(x,t), \quad t \in…
Dispersive estimates for the Schrödinger equation with finite rank perturbations
Han Cheng, Shanlin Huang, Quan Zheng
In this paper, we investigate dispersive estimates for the time evolution of Hamiltonians $$ H=-Δ+\sum_{j=1}^N\langle\cdot\,, φ_j\rangle φ_j\quad\,\,\,\text{in}\,\,\,\mathbb{R}^d,\…