论文标题
$ l^p $ - 绑定了2Dschrödinger操作员的Wave Operators具有点互动
$L^p$-boundedness of wave operators for 2D Schrödinger operators with point interactions
论文作者
论文摘要
对于二维Schrödinger运营商$ h $与点交互作用，我们证明了$（h，h_0）$（h，h_0）$，$ h_0 $作为免费的schrödinger运算符的散射浪潮操作员在lebesgue space $ l^p（\ r^2）$中是$ 1 <p <p <p <p <p <p <满足$ u（x）= c | x |^{ - 1}+ o（| x |^{ - 1}）$ as $ | x | \ to \ infty $，$ c \ not = 0 $。否则，它们以$ 1 <p \ leq 2 $的限制，并以$ 2 <p <\ infty $而无限。
For two dimensional Schrödinger operator $H$ with point interactions, We prove that wave operators of scattering for the pair $(H,H_0)$, $H_0$ being the free Schrödinger operator, are bounded in the Lebesgue space $L^p(\R^2)$ for $1<p<\infty$ if and only if there are no generalized eigenfunctions of $Hu(x)=0$ which satisfy $u(x)= C|x|^{-1}+ o(|x|^{-1})$ as $|x|\to \infty$, $C\not=0$. Otherwise they are bounded for $1<p\leq 2$ and unbounded for $2<p<\infty$.
