Structure of wave operators for a scaling-critical class of potentials
Structure of wave operators for a scaling-critical class of potentials
We prove a structure formula for the wave operators in ${\Bbb R}^3 $$W_{\pm} = \mathop{\hbox{s-lim}}\limits_{t\to\pm\infty} e^{it (-\Delta + V)} P_c e^{it\Delta}$$ and their adjoints for a scaling-invariant class of scalar potentials $V \in B$, $$B = \left\{V\mid\sum_{k\in\Bbb{Z}} 2^{k/2} \big\|\chi_{|x|\in [2^k, 2^{k+1}]}(x) V(x)\big\|_{L^2} < \infty\right\},$$ under the assumption that zero is …