论文标题
一般左定理论的观点
Perspectives on General Left-Definite Theory
论文作者
论文摘要
2002年，利特尔·约翰（Littlejohn）和韦尔曼（Wellman）为半结合的自身伴侣操作员开发了著名的一般左定义理论，并在差异操作员上使用了许多应用。该理论始于半结合的自动伴侣操作员，并构建了与初始操作员的力量密切相关的相关Hilbert空间和自动接合操作员的连续体。该发展刺激了当今仍在进行的一系列活动。 该说明性的主要目标（除命题外1）手稿是比较和对比一般左定义理论的互补理论，即自相关扩展和奇异扰动理论的Birman-Krein-vishik（BKV）理论。通过这种方式，我们希望鼓励人们对左定理论的兴趣，并指出互连领域相互联系的潜在增长方向。我们包括几个相关的开放问题，以进一步进一步实现这些目标。
In 2002, Littlejohn and Wellman developed a celebrated general left-definite theory for semi-bounded self-adjoint operators with many applications to differential operators. The theory starts with a semi-bounded self-adjoint operator and constructs a continuum of related Hilbert spaces and self-adjoint operators that are intimately related with powers of the initial operator. The development spurred a flurry of activity in the field that is still ongoing today. The main goal of this expository (with the exception of Proposition 1) manuscript is to compare and contrast the complementary theories of general left-definite theory, the Birman--Krein--Vishik (BKV) theory of self-adjoint extensions and singular perturbation theory. In this way, we hope to encourage interest in left-definite theory as well as point out directions of potential growth where the fields are interconnected. We include several related open questions to further these goals.
