Limiting Absorption Principle and Radiation Condition for Repulsive Hamiltonians
Limiting Absorption Principle and Radiation Condition for Repulsive Hamiltonians
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排斥哈密顿量的极限吸收原理和辐射条件
DOI：
10.1619/fesi.64.199
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
K. Itakura
中科院分区：
文献类型：
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作者：
K. Itakura
对于球对称的排斥哈密顿量，我们证明了Besov界，辐射条件界和限制吸收原理。索末菲唯一性的结果也遵循这些作为推论。特别地，本文考虑的哈密顿量涵盖了倒谐振子的情况。在定理的证明中，我们主要使用了Ito和Skibsted最近发明的一个交换子论证。这一论证简单而初级，没有采用能量截断或微局域分析。
For spherically symmetric repulsive Hamiltonians we prove the Besov bound, the radiation condition bounds and the limiting absorption principle. The Sommerfeld uniqueness result also follows as a corollary of these. In particular, the Hamiltonians considered in this paper cover the case of inverted harmonic oscillator. In the proofs of our theorems, we mainly use a commutator argument invented recently by Ito and Skibsted. This argument is simple and elementary, and dose not employ energy cut-offs or the microlocal analysis.