The absolutely continuous spectrum of Jacobi matrices
The absolutely continuous spectrum of Jacobi matrices
复制标题
雅可比矩阵的绝对连续谱
DOI：
10.4007/annals.2011.174.1.4
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
C. Remling
中科院分区：
文献类型：
--
作者：
C. Remling
我探讨了Breimesser和Pearson关于一维Schr“odinger算子的绝对连续谱的一个开创性结果的一些后果。这些包括预言的潜力和相当一般的结果，对某些极限潜力的方法的甲骨文定理。特别地，我们证明了一般有限间隙情况下的Denisov-Rakhmanov型定理。
主要内容如下：在一维空间中产生绝对连续的谱是极其困难的，因此它的存在具有强烈的含义。
I explore some consequences of a groundbreaking result of Breimesser and Pearson on the absolutely continuous spectrum of one-dimensional Schr"odinger operators. These include an Oracle Theorem that predicts the potential and rather general results on the approach to certain limit potentials. In particular, we prove a Denisov-Rakhmanov type theorem for the general finite gap case.
The main theme is the following: It is extremely difficult to produce absolutely continuous spectrum in one space dimension and thus its existence has strong implications.