论文标题
单参数半群和应用的规范视野扰动
Norm-ideal perturbations of one-parameter semigroups and applications
论文作者
论文摘要
基于Dyson扩展的融合的单参数半群发电机的等效类别的概念可以追溯到Hille和Phillips的开创性工作，Hille和Phillips的开创性作品在1957年的第十二章中，他们的功能分析专着专着的第十三章中，详细介绍了理论。遵循他们将dyson扩展作为中心对象的方法，在本文的第一部分中，我们研究了相对于希尔伯特空间上的Schatten-von Neumann理想的发电机扰动的一般框架。这使我们能够在发电机上开发一个等级的等效关系家族，该家族完善了经典的概念，并为扰动系列的尾部提供了比预期的融合特性。然后，我们展示该框架如何在非自我辅助施罗宾格运营商的上下文中实现。
The notion of equivalence classes of generators of one-parameter semigroups based on the convergence of the Dyson expansion can be traced back to the seminal work of Hille and Phillips, who in Chapter XIII of the 1957 edition of their Functional Analysis monograph, developed the theory in minute detail. Following their approach of regarding the Dyson expansion as a central object, in the first part of this paper we examine a general framework for perturbation of generators relative to the Schatten-von Neumann ideals on Hilbert spaces. This allows us to develop a graded family of equivalence relations on generators, which refine the classical notion and provide stronger-than-expected properties of convergence for the tail of the perturbation series. We then show how this framework realises in the context of non-self-adjoint Schrodinger operators.
