Radiation condition bounds on manifolds with ends
Radiation condition bounds on manifolds with ends
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带末端流形的辐射条件边界
DOI：
10.1016/j.jfa.2019.108449
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发表时间：
2020
影响因子：
1.7
通讯作者：
Skibsted E.
中科院分区：
文献类型：
--
作者：
Ito K.;Skibsted E.
我们研究了具有逃逸函数的流形上薛定谔算子的谱理论。一类特殊的例子是具有欧几里得和/或双曲端点的流形。某些外部域可能无界障碍物包括在内。我们证明了Rellich定理，限制吸收原理，辐射条件的界限和索末菲唯一性结果，努力扩展和细化以前已知的频谱流形上的结果。证明是由广泛使用的换向器参数。这些论点有一个经典的精神（本质上）不涉及能量截止或微局部分析，并要求，大概，最小的正则性和衰变性质的扰动。这篇论文有它自己的兴趣，但它也作为在续集[19]中充分发展的稳态散射理论的基础。
We study spectral theory for the Schrödinger operator on manifolds possessing an escape function. A particular class of examples are manifolds with Euclidean and/or hyperbolic ends. Certain exterior domains for possibly unbounded obstacles are included. We prove Rellich's theorem, the limiting absorption principle, radiation condition bounds and the Sommerfeld uniqueness result, striving to extending and refining previously known spectral results on manifolds. The proofs are given by an extensive use of commutator arguments. These arguments have a classical spirit (essentially) not involving energy cutoffs or microlocal analysis and require, presumably, minimum regularity and decay properties of perturbations. This paper has interest of its own right, but it also serves as a basis for the stationary scattering theory developed fully in the sequel [19].