通过其逆的实部分量研究算子的Schatten指数
Schatten index of the operator via the real component of its inverse
AI总结：
本文通过算子逆的Hermitian实部分量性质，利用渐近公式估计奇异值，完整刻画非自伴离散谱算子属于Schatten类的条件，并应用于分数阶演化方程。
摘要：
本文研究具有离散谱的非自伴算子的谱性质。主要挑战在于通过Hermitian实部分量的性质完整刻画其属于Schatten类的条件。借助已建立的渐近公式，我们详细阐述了奇异值的估计方法。这一基础性结果具有重要优势，因为许多理论陈述都建立在其上，其中之一是关于根向量级数展开的概念，该概念在演化方程理论中有着广泛的应用。在此背景下，我们考虑了分数阶演化方程，其中算子位于不含时间变量的项中。文中考察了具体的著名算子，并明确展示了所提方法的优越性。
英文摘要：
In this paper we study spectral properties of non-selfadjoint operators with the discrete spectrum. The main challenge is to represent a complete description of belonging to the Schatten class through the properties of the Hermitian real component. The method of estimating the singular values is elaborated by virtue of the established asymptotic formulas. The latter fundamental result is advantageous since many theoretical statements based upon it, one of them is a concept on the root vectors series expansion which leads to a wide spectrum of applications in the theory of evolution equations. In this regard the evolution equations of fractional order with the operator in the term not containing the time variable are involved. The concrete well-known operators are considered and the advantage of the represented method is convexly shown.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
