Abstract

In this paper, it is investigated that necessary and sufficient conditions for a minimal operator defined by a degenerate first-order differential operator expression in the Hilbert space \(L_{2}(H,(a,b)),\,a,b\in\mathbb{R}\) to be formally normal. Also, all normal extensions of the minimal operator are given with their domains. Moreover, the spectrum set of these normal extensions is given through the family of evolution operators.

中文翻译：

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简并一阶微分算子的正规扩展

 抽象的

本文研究了希尔伯特空间中简并一阶微分算子表达式定义的最小算子的充要条件\(L_{2}(H,(a,b)),\,a, b\in\mathbb{R}\) 是形式正规的。此外，最小算子的所有正常扩展都给出了它们的域。此外，这些正常扩展的频谱集是通过演化算子族给出的。