Convergence properties for generalized Schroedinger operators along tangential curves

Tencent Meeting ID: 118-861-553

Abstract: 

In this paper, we consider convergence properties for generalized Schr\{o}dinger operators along tangential curves in $\mathbb{R}^{n} \times \mathbb{R}$ with less smoothness comparing with Lipschitz condition. Firstly, we obtain sharp convergence rate for generalized Schr\{o}dinger operators with polynomial growth along tangential curves in $\mathbb{R}^{n} \times \mathbb{R}$, $n \ge 1$. Secondly, it was open until now on pointwise convergence of solutions to the Schr\{o}dinger equation along non-$C^1$ curves in $\mathbb{R}^{n} \times \mathbb{R}$, $n\geq 2$, we obtain the corresponding results along