5 papers
Observability and controllability for the Schrödinger equation on polyhedra
Wei Qu, Zhiwen Duan
We consider the observability and controllability for the Schrödinger equation on polyhedra. We show that for the Schrödinger equation on convex polyhedra in $\mathbb{R}^d\,(d\geq2…
Fractal Uncertainty and Quantitative Uniqueness for the Fourier Bessel Transform
Xingyu Zhao, Longben Wei, Zhiwen Duan
We establish quantitative uniqueness and a fractal uncertainty principle for the Fourier Bessel transform. In arbitrary dimension, we prove a quantitative uniqueness estimate on re…
Time-Dependent Potential Recovery from Local Data on Conformally Transversally Anisotropic Manifolds
Yujian Zheng, Zhiwen Duan, Shiqi Jing
We study the recovery of a time-dependent potential in a parabolic equation on a conformally transversally anisotropic manifold. The initial state and a lateral Dirichlet datum sup…
Almost everywhere convergence of Bochner-Riesz means for the Hermite type Laguerre expansions
Longben Wei, Zhiwen Duan
Consider the space equipped with Euclidean distance and the Lebesgue measure. For every , we consider the Hermite-L…
Observability and unique continuation inequalities for the Schrödinger equations with inverse-square potentials
Hui Xu, Longben Wei, Zhiwen Duan
This paper is inspired by Wang, Wang and Zhang's work [ Observability and unique continuation inequalities for the Schrödinger equation. J. Eur. Math. Soc. 21, 3513--3572 (2019)],…