The limiting absorption principle for the discrete Wigner-von Neumann operator

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• 作者：Marc-Adrien Mandich ^{marc-adrien.mandich@u-bordeaux.fr}
• 关键词：39A70 ; 81Q10 ; 47B25 ; 47A10
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：272
• 期：6
• 页码：2235-2272
• 全文大小：648 K
• 卷排序：272

文摘

We apply weighted Mourre commutator theory to prove the limiting absorption principle for the discrete Schrödinger operator perturbed by the sum of a Wigner–von Neumann and long-range type potential. In particular, this implies a new result concerning the absolutely continuous spectrum for these operators even for the one-dimensional operator. We show that methods of classical Mourre theory based on differential inequalities and on the generator of dilation cannot apply to the aforementioned Schrödinger operators.