Applications of Resonance Theory Without Analyticity Assumption
Applications of Resonance Theory Without Analyticity Assumption
复制标题
无解析性假设的共振理论的应用
DOI：
10.1007/s00023-021-01065-w
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
T. Ramond
中科院分区：
文献类型：
--
作者：
J. Bony;L. Michel;T. Ramond
我们证明了散射理论中涉及共振的结果对于非解析势仍然有效，即使共振的概念在此设置中没有定义。更准确地说，我们表明，如果一个半经典薛定谔算子的潜力被认为是光滑的，并在无穷远处减少，通常的公式有关的散射量和共振仍然成立。证明的主要成分是一个新类型的预解估计，有关的预解算子与其截断对应的预解。
We prove that the results in scattering theory that involve resonances are still valid for non-analytic potentials, even if the notion of resonance is not defined in this setting. More precisely, we show that if the potential of a semiclassical Schrödinger operator is supposed to be smooth and to decrease at infinity, the usual formulas relating scattering quantities and resonances still hold. The main ingredient for the proofs is a resolvent estimate of a new type, relating the resolvent of an operator with the resolvent of its cut-off counterpart.