论文标题
非本地Schrödinger操作员短期和远程电位之间的阈值
Threshold between short and long-range potentials for non-local Schrödinger operators
论文作者
论文摘要
我们为非本地Schrödinger运算符的散射理论开发了由Laplacian的函数定义的，其中包括其分数功率$（-Δ）^ρ$，$ 0 <ρ\ leqslant1 $。特别是，我们的功能属于比伯恩斯坦函数集更宽的类别。通过显示波算子的存在和不存在，我们阐明了扰动电位的短期和远程衰减条件之间的阈值。
We develop scattering theory for non-local Schrödinger operators defined by functions of the Laplacian that include its fractional power $(-Δ)^ρ$ with $0<ρ\leqslant1$. In particular, our function belongs to a wider class than the set of Bernstein functions. By showing the existence and non-existence of the wave operators, we clarify the threshold between the short and long-range decay conditions for perturbational potentials.
