Abstract We study spectral theory for the Schrodinger 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] .

中文翻译：

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带末端的流形上的辐射条件界限

摘要 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/或双曲线端的流形。包括可能无限障碍的某些外部域。我们证明了 Rellich 定理、极限吸收原理、辐射条件界限和 Sommerfeld 唯一性结果，努力扩展和改进先前已知的流形光谱结果。证明是通过广泛使用交换器参数给出的。这些论点具有经典精神（基本上）不涉及能量截止或微局域分析，并且可能需要扰动的最小规律性和衰减特性。这篇论文有它自己的兴趣，