Speaker：Jian Wang (Fujian Normal University)

Time：2024-8-24, 10:00

Location：Room C503 & Tencent Meeting ID：652-132-498（No Password）

Abstract:

We establish global two-sided heat kernel estimates (for full time and space) of the Schr\"odinger operator $-\frac{1}{2}\Delta+V$ on $\R^d$, where the potential $V(x)$ is locally bounded and behaves like $c|x|^{-\alpha}$ near infinity with $\alpha\in (0,2)$ and $c> 0$, or with $\alpha>0$ and $c<0 $.

Our results improve all known results in the literature, and it seems that this is the first time that consistent two-sided heat kernel bounds for the long range potentials are established.