Abstract

In this paper, by using the methods of the operator theory, the general form of all compactly solvable extension of the minimal operator which is generated by the first order linear differential operator expression in the Hilbert spaces of vector-functions on finite interval has been found. Later on, the spectrum set of the compactly solvable extensions has been investigated. In addition, the asymptotical behavior of the eigenvalues of any inverse of compactly solvable extension has been studied. Finally, the necessary and sufficient condition for the inverse of the compactly solvable extensions to be belong to Schatten–von Neumann classes has been given.

中文翻译：

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关于一阶紧可解微分算子

摘要

在本文中，通过算子理论的方法，找到了矢量函数的希尔伯特空间中一阶线性微分算子表达式生成的最小算子的所有紧可解扩展的一般形式。 。后来，研究了紧密可解扩展的谱集。此外，已经研究了任何可紧解可逆扩展的特征值的渐近行为。最后，给出了紧可解扩展的逆属于Schatten–von Neumann类的充要条件。