Title: Unique Continuation through Hyperplane for Higher Order Parabolic and Shrödinger Equations,
Abstract: We consider higher order parabolic operator $\partial_t+(-\Delta_x)^m$ and
higher order Schrödinger operator $i^{-1}\partial_t+(-\Delta_x)^m$ in
$X=\{(t,x)\in\mathbb{R}^{1+n};~|t|<A,|x_n|<B\}$ where $m$ is any positive
integer. Under certain lower order and regularity assumptions, we prove that if
the solution for linear problem vanishes when $x_n>0$, then the solution
vanishes in $X$. Such results are given globally, and we also prove some
related local results.