论文标题
限制具有Wigner-von neumann潜力和缓慢衰减电位的离散Schr {Ö} dinger操作员的吸收原理
Limiting absorption principle for discrete Schr{ö}dinger operators with a Wigner-von Neumann potential and a slowly decaying potential
论文作者
论文摘要
我们考虑$ {\ Mathbb {z}}^d $上的离散schr {Ö} dinger运算符，其中扰动由远程类型电位和wigner-von neumann类型电位组成。我们仍在加权穆雷理论的框架中工作，我们改善了在[MA1]中获得的限制吸收原理（LAP）。据我们所知，即使在一维情况下，这也是一个新的结果。改进包括对远程潜力的假设削弱和更好的膝盖重量。改进仅依赖于以下事实：扩张的发生器（用作共轭操作员）是位置操作员从上方界定的。为了利用这一点，调用了Loewner的操作器单调函数定理。
We consider discrete Schr{ö}dinger operators on ${\mathbb{Z}}^d$ for which the perturbation consists of the sum of a long-range type potential and a Wigner-von Neumann type potential. Still working in a framework of weighted Mourre theory, we improve the limiting absorption principle (LAP) that was obtained in [Ma1]. To our knowledge, this is a new result even in the one-dimensional case. The improvement consists in a weakening of the assumptions on the long-range potential and better LAP weights. The improvement relies only on the fact that the generator of dilations (which serves as conjugate operator) is bounded from above by the position operator. To exploit this, Loewner's theorem on operator monotone functions is invoked.
