论文标题
在第四阶的schrödinger操作员的$ l^p $界限上
On the $L^p$ boundedness of the Wave Operators for fourth order Schrödinger operators
论文作者
论文摘要
我们考虑第四阶Schrödinger运算符$ h =δ^2+v（x）$在三个维度上，具有实值的潜在$ v $。令$ h_0 =δ^2 $，如果$ v $衰减充足，并且在绝对连续的频谱中没有特征值或共鸣，则Wave Operators $ W _ {\ PM} = S \， - \， - \，\，\ lim_ { $ l^p（\ Mathbb r^3）$ for $ 1 <p <\ infty $。
We consider the fourth order Schrödinger operator $H=Δ^2+V(x)$ in three dimensions with real-valued potential $V$. Let $H_0=Δ^2$, if $V$ decays sufficiently and there are no eigenvalues or resonances in the absolutely continuous spectrum of $H$ then the wave operators $W_{\pm}= s\,-\,\lim_{t\to \pm \infty} e^{itH}e^{-itH_0}$ extend to bounded operators on $L^p(\mathbb R^3)$ for all $1<p<\infty$.
