论文标题
施罗丁格型运算符的最小速度与分数功率
Minimal velocity bound for Schroedinger-type operator with fractional powers
论文作者
论文摘要
在散射理论中已知，最小速度结合在证明波算子的渐近完整性方面起着结论性的作用。在这项研究中，我们证明了具有分数功率的两体Schroedinger型操作员的最小速度结合和其他重要估计值。我们假设成对电位函数属于包括远距离衰减和库仑型局部奇异性的广泛类别。预计我们的估计值将用于证明在各种（不仅是短期和远程和N体）情况下的分数Schroedinger型操作员的渐近完整性。
It is known in scattering theory that the minimal velocity bound plays a conclusive role in proving the asymptotic completeness of the wave operators. In this study, we prove the minimal velocity bound and other important estimates for the two-body Schroedinger-type operator with fractional powers. We assume that the pairwise potential functions belong to broad classes that include long-range decay and Coulomb-type local singularities. Our estimates are expected to be applied to prove the asymptotic completeness for the fractional Schroedinger-type operators in various (not only short-range but also long-range and N-body) situations.
