3 papers
math.AP2024
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…
math.AP2024
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…
math.AP2022
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,\…