The absolutely continuous spectrum of Jacobi matrices

研究了具有绝对连续谱的雅可比矩阵的一般结构性质。这一分析的起点是最近发现的一个事实，即存在一种相当特殊类型的通用构件，并且具有必须用来产生任何类型的绝对连续谱的特殊性质。更准确地说，这个角色是由无反射操作员扮演的，这些操作员将在我们的调查中占据中心舞台。我们想分析它们的性质，以及与移位图有关的动力学性质。谱理论是量子力学数学理论和我们对物质理解的核心。上面概述的计划涉及这些理论的数学问题。虽然这些都属于基础研究领域，但它们也与物理和材料科学的潜在长期应用有着密切的联系。

We study general structural properties of Jacobi matrices with some absolutely continuous spectrum. The starting point of this analysis is the recently discovered fact that there are universal building blocks of a rather special type, and with peculiar poperties that have to be used to produce any kind of absolutely continuous spectrum. More precisely, this role is played by reflectionless operators, and these will take center stage in our investigations. We would like to analyze their properties and their dynamical properties associated with the shift map.Spectral theory is at the heart of the mathematical theory of quantum mechanics and our understanding of matter. The plan outlined above concerns mathematical issues of these theories. While these belong to the domain of fundamental research, there are also close connections to physics and potential long term applications in materials science.