We develop a new scheme of proofs for spectral theory of the N-body Schrödinger operators, reproducing and extending a series of sharp results under minimum conditions. Our main results include Rellich’s theorem, limiting absorption principle bounds, microlocal resolvent bounds, Hölder continuity of the resolvent and a microlocal Sommerfeld uniqueness result. We present a new proof of Rellich’s theorem which is unified with exponential decay estimates studied previously only for L2-eigenfunctions. Each pair-potential is a sum of a long-range term with first-order derivatives, a short-range term without derivatives and a singular term of operator- or form-bounded type, and the setup includes hard-core interaction. Our proofs consist of a systematic use of commutators with ‘zeroth order’ operators. In particular, they do not rely on Mourre’s differential inequality technique.

中文翻译：

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N体薛定谔算子谱理论的新方法

我们为光谱理论开发了一种新的证明方案ñ-body Schrödinger 算子，在最小条件下再现和扩展一系列尖锐的结果。我们的主要结果包括 Rellich 定理、限制吸收原理边界、微局部分解边界、分解的 Hölder 连续性和微局部 Sommerfeld 唯一性结果。我们提出了 Rellich 定理的新证明，它与以前研究的指数衰减估计相统一大号2-特征函数。每个对势是具有一阶导数的长期项、没有导数的短期项和算子或形式有界类型的奇异项的总和，并且设置包括核心交互。我们的证明包括系统地使用带有“零阶”运算符的交换器。特别是，它们不依赖于 Mourre 的微分不等式技术。