Abstract

In this paper, certain spectral properties related with the first order linear differential expression in the weighted Hilbert space at finite interval have been examined. Firstly, the minimal and maximal operators which are generated by the first order linear differential expression in the weighted Hilbert space have been determined. Then, the deficiency indices of the minimal operator have been calculated. Moreover, a space of boundary values of the minimal operator has been constructed. Afterwards, by using the Calkin–Gorbachuk’s method, the general form of all maximally dissipative extensions of the minimal operator in terms of boundary values has been found. Later on, the structure of spectrum of these extensions has been investigated.

中文翻译：

---

加权希尔伯特空间中的一阶极大耗散微分算子

摘要

在本文中，研究了在有限间隔内加权希尔伯特空间中与一阶线性微分表达式有关的某些光谱特性。首先，确定了由加权希尔伯特空间中的一阶线性微分表达式生成的最小和最大算子。然后，计算了最小算子的缺陷指数。此外，已经构造了最小算子的边界值的空间。然后，通过使用Calkin–Gorbachuk方法，找到了最小算子在边界值方面的所有最大耗散扩展的一般形式。后来，对这些扩展的光谱结构进行了研究。