Spectral analysis of the matrix Sturm–Liouville operator

被引：0

作者：

Natalia P. Bondarenko

机构：

[1] Samara National Research University,Department of Applied Mathematics and Physics

[2] Saratov State University,Department of Mechanics and Mathematics

来源：

Boundary Value Problems | / 2019卷

关键词：

Matrix Sturm–Liouville operator; General self-adjoint boundary condition; Eigenvalue asymptotics; Asymptotics of weight matrices; Sturm–Liouville operators on graphs; 34B09; 34B24; 34B45; 34L20; 34L40;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The self-adjoint matrix Sturm–Liouville operator on a finite interval with a boundary condition in general form is studied. We obtain asymptotic formulas for the eigenvalues and the weight matrices of the considered operator. These spectral characteristics play an important role in the inverse spectral theory. Our technique is based on an analysis of analytic functions and on the contour integration in the complex plane of the spectral parameter. In addition, we adapt the obtained asymptotic formulas to the Sturm–Liouville operators on a star-shaped graph with two different types of matching conditions.

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