论文标题
具有分布系数的高阶差分运算符的光谱数据渐近差异
Spectral data asymptotics for the higher-order differential operators with distribution coefficients
论文作者
论文摘要
在本文中，对于具有分布系数和分离的边界条件的高阶差分运算符获得了光谱数据（特征值和重量数）的渐近学。此外，我们考虑了两个边界值问题的情况，即差分表达式的某些系数和边界条件的重合。在这种情况下，我们估计了它们的光谱数据的差异。 尽管对于具有规则（可集成）系数的差异操作员，光谱数据的渐近行为是对作者所知的最佳差异操作员进行了充分研究的，但是对于具有一般形式的分布系数（广义函数）的高阶差异算子，没有结果的结果。本文的技术依赖于最近获得的正则化和具有分布系数的差异操作员的Birkhoff型解决方案。我们的结果适用于反光谱问题的理论以及单独的意义。
In this paper, the asymptotics of the spectral data (eigenvalues and weight numbers) are obtained for the higher-order differential operators with distribution coefficients and separated boundary conditions. Additionally, we consider the case when, for the two boundary value problems, some coefficients of the differential expressions and of the boundary conditions coincide. We estimate the difference of their spectral data in this case. Although the asymptotic behaviour of spectral data is well-studied for differential operators with regular (integrable) coefficients, to the best of the author's knowledge, there were no results in this direction for the higher-order differential operators with distribution coefficients (generalized functions) in a general form. The technique of this paper relies on the recently obtained regularization and the Birkhoff-type solutions for differential operators with distribution coefficients. Our results have applications to the theory of inverse spectral problems as well as a separate significance.
