The Absolutely Continuous Spectrum of One-dimensional Schrödinger Operators
The Absolutely Continuous Spectrum of One-dimensional Schrödinger Operators
复制标题
一维薛定谔算子的绝对连续谱
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
C. Remling
中科院分区：
文献类型：
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作者：
C. Remling
本文研究了具有某些绝对连续谱的一维薛定谔算子的一般结构性质。基本结果表明，在谱测度的绝对连续部分的支撑下，移位映射下的势的ω极限点是无反射的。这意味着这样的潜力和Denisov-Rakhmanov型定理的甲骨文定理。在离散情况下，对于Jacobi算子，这些问题在我最近的论文中进行了讨论（Remling，The absolutely continuous spectrum of Jacobi matrices，http：//arxiv.org/abs/0706.1101，2007）。本文对连续情形的处理依赖于相同的基本思想。
This paper deals with general structural properties of one-dimensional Schrödinger operators with some absolutely continuous spectrum. The basic result says that the ω limit points of the potential under the shift map are reflectionless on the support of the absolutely continuous part of the spectral measure. This implies an Oracle Theorem for such potentials and Denisov-Rakhmanov type theorems. In the discrete case, for Jacobi operators, these issues were discussed in my recent paper (Remling, The absolutely continuous spectrum of Jacobi matrices, http://arxiv.org/abs/0706.1101, 2007). The treatment of the continuous case in the present paper depends on the same basic ideas.