One-Dimensional Ergodic Schrödinger Operators
One-Dimensional Ergodic Schrödinger Operators
复制标题
一维遍历薛定谔算子
DOI：
10.1090/gsm/221
复制
发表时间：
2022
期刊：
影响因子：
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通讯作者：
J. Fillman
中科院分区：
文献类型：
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作者：
D. Damanik;J. Fillman
一维遍历算子的理论包含了动力系统、拓扑学和分析学思想的完美综合。此外，该设置包括许多物理感兴趣的模型，包括那些模拟晶体、无序介质或准晶体的算子。近几十年来，这一领域取得了重大进展，其中大部分尚未在教科书中讨论。从一个在谱理论的关键主题复习开始，本卷介绍了动态定义的潜力离散一维薛定谔算子的基本理论。它还包括一个自我包含的介绍遍历理论和拓扑动力学的相关方面。这份文本是访问研究生谁已经完成了一个学期的课程在测量理论和复杂的分析。它的目的是作为初级研究人员和开始研究生领域的介绍，以及已经在这一领域工作的人的参考文本。它非常适合自学，并包含许多练习（许多都有提示）。
The theory of one-dimensional ergodic operators involves a beautiful synthesis of ideas from dynamical systems, topology, and analysis. Additionally, this setting includes many models of physical interest, including those operators that model crystals, disordered media, or quasicrystals. This field has seen substantial progress in recent decades, much of which has yet to be discussed in textbooks. Beginning with a refresher on key topics in spectral theory, this volume presents the basic theory of discrete one-dimensional Schrödinger operators with dynamically defined potentials. It also includes a self-contained introduction to the relevant aspects of ergodic theory and topological dynamics. This text is accessible to graduate students who have completed one-semester courses in measure theory and complex analysis. It is intended to serve as an introduction to the field for junior researchers and beginning graduate students as well as a reference text for people already working in this area. It is well suited for self-study and contains numerous exercises (many with hints).