论文标题
与特殊的laguerre差异表达式相关的自聚会扩展的光谱
The Spectrum of Self-Adjoint Extensions associated with Exceptional Laguerre Differential Expressions
论文作者
论文摘要
特殊的laguerre型差异表达式组成了具有理性电位和一个极限圈子端点的无限类别。在此手稿中，通过将表达与经典的laguerre差异表达相关的darboux变换给出了一般特殊laguerre型差异表达的所有自相关扩展的光谱。该光谱是从明确的Weyl $ m $功能中提取的，直到标志。 该构建主要依赖于两个工具：边界三元组，该工具将自相关扩展的参数化并产生Weyl $ m $ functions，以及对Maya图和分区的操作，这些图表和分区对定义相关的Darboux变换的种子函数进行了分类。列出了几个例子。
Exceptional Laguerre-type differential expressions make up an infinite class of Schrödinger operators having rational potentials and one limit-circle endpoint. In this manuscript, the spectrum of all self-adjoint extensions for a general exceptional Laguerre-type differential expression is given in terms of the Darboux transformations which relate the expression to the classical Laguerre differential expression. The spectrum is extracted from an explicit Weyl $m$-function, up to a sign. The construction relies primarily on two tools: boundary triples, which parameterize the self-adjoint extensions and produce the Weyl $m$-functions, and manipulations of Maya diagrams and partitions, which classify the seed functions defining the relevant Darboux transforms. Several examples are presented.
