反射的谱定义与动力学定义的等价性
Equality of the Spectral and Dynamical Definitions of Reflection
摘要：
对于全线雅可比矩阵，薛定谔算子，和CMV矩阵，我们表明，是无反射，在这个意义上的$m$ -功能的众所周知的属性，相当于一个缺乏反射的动力学意义上的任何状态，完全$x=-\infty$作为$t\to -\infty $去完全$x=\infty$作为$t\to\infty$。这使我们能够解决一个猜想Deift和西蒙从1983年关于遍历雅可比矩阵。
英文摘要：
For full-line Jacobi matrices, Schrödinger operators, and CMV matrices, we show that being reflectionless, in the sense of the well-known property of $m$-functions, is equivalent to a lack of reflection in the dynamics in the sense that any state that goes entirely to $x=-\infty$ as $t\to -\infty $ goes entirely to $x=\infty$ as $t\to\infty$. This allows us to settle a conjecture of Deift and Simon from 1983 regarding ergodic Jacobi matrices.
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