15 citations · 25 across the 6 of their papers we have counts for
6 papers
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…
The scattering of fractional Schrödinger operators with short range potentials
Rui Zhang, Tianxiao Huang, Quan Zheng
For any positive real number , we study the scattering theory in a unified way for the fractional Schrödinger operator , where and the real-valued p…
Unique continuation properties for one dimensional higher order Schrödinger equations
Tianxiao Huang, Shanlin Huang, Quan Zheng
We study two types of unique continuation properties for the higher order Schrödinger equation with potential $$ i\partial_tu=(-Δ_x)^mu+V(t,x)u,\quad(t,x)\in\mathbb{R}^{1+n},\,2\le…
Unique continuation through hyperplane for higher order parabolic and Schrödinger equations
Tianxiao Huang
Consider the higher order parabolic operator and the higher order Schrödinger operator in $X=\{(t,x)\in\mathbb{R}^{1+n};~|t|<A,|x_…
Inhomogeneous Oscillatory Integrals and Global Smoothing Effects for Dispersive Equations
Tianxiao Huang, Shanlin Huang, Quan Zheng
We study oscillatory integrals of the type where is a general function satisfying some elliptic type and non-degenerate conditions a…