论文标题
在圆圈上真实主要类型运算符的经典和量子完整性的等效性
Equivalence of classical and quantum completeness for real principal type operators on the circle
论文作者
论文摘要
在本文中，我们证明了汉密尔顿流量和基本自我相关性的完整性对于圈子上的真实主要类型运算符是等效的。此外，我们研究这些操作员的光谱特性。该证明是基于具有非真实特征值的本征函数的构建，这在散射理论中众所周知。此外，解释了散射理论与基本自我相关性之间的关系。
In this article, we prove that the completeness of the Hamilton flow and essential self-adjointness are equivalent for real principal type operators on the circle. Moreover, we study spectral properties of these operators. The proof is based on the construction of eigenfunctions with non-real eigenvalues which is well-known in scattering theory. Moreover, the relationship between scattering theory and the essential self-adjointness is explained.
