4 papers
Fractal Remez inequality on the sphere and observability of the heat equation
Xinyi Chen, Shanlin Huang
This paper is concerned with Remez-type inequalities and their applications in observability inequality. Our aim is twofold. First, we establish the following fractal Remez's inequ…
Dynamical versions of Morgan's Uncertainty Principle and Electromagnetic Schrödinger Evolutions
Shanlin Huang, Zhenqiang Wang
This paper investigates the unique continuation properties of solutions of the electromagnetic Schrödinger equation $$ i\partial_{t}u(x,t)+(\nabla-i A)^{2}u(x,t)=V(x,t)u(x,t)\,\,\,…
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 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…