Tianxiao Huang

collaborators

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 $n$ and any integer $m \geq 1$ with $n > 4 m$ , 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-ph2020

The scattering of fractional Schrödinger operators with short range potentials

Rui Zhang, Tianxiao Huang, Quan Zheng

For any positive real number $s$ , we study the scattering theory in a unified way for the fractional Schrödinger operator $H = H_{0} + V$ , where $H_{0} = (- Δ)^{\frac{s}{2}}$ and the real-valued p…