AN OVERVIEW OF PERIODIC ELLIPTIC OPERATORS
AN OVERVIEW OF PERIODIC ELLIPTIC OPERATORS
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DOI：
10.1090/bull/1528
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发表时间：
2016-07-01
影响因子：
1.3
通讯作者：
Kuchment, Peter
中科院分区：
文献类型：
--
作者：
Kuchment, Peter
本文综述了数学物理和其他领域中出现的周期算子理论的主要主题、技术和结果。研究了Bloch变元和Fermi变元的解析性质，它们对这类算子的大部分谱特征有重要影响.所描述的方法不仅适用于具有周期电势的薛定谔算子的标准模型--Delta+V(X)，而且适用于各种椭圆周期方程和系统、图上的方程、杆算子上的(偏导数)以及紧基的阿贝尔覆盖上的其他算子.文中提到了重要的应用.然而，由于大小的限制，它们没有得到详细的处理。
The article surveys the main topics, techniques, and results of the theory of periodic operators arising in mathematical physics and other areas. Close attention is paid to studying analytic properties of Bloch and Fermi varieties, which significantly influence most spectral features of such operators.The approaches described are applicable not only to the standard model example of Schrodinger operator with periodic electric potential -Delta+V(x), but to a wide variety of elliptic periodic equations and systems, equations on graphs, (partial derivative) over bar -operator, and other operators on abelian coverings of compact bases.Important applications are mentioned. However, due to the size restrictions, they are not dealt with in detail.