ESTIMATES OF LARGE EIGENVALUES AND TRACE FORMULA FOR THE VECTORIAL STURM-LIOUVILLE EQUATIONS

被引：0

作者：

Yang, Chuan-Fu ^{[1
]}

Huang, Zhen-You ^{[1
]}

Yang, Xiao-Ping ^{[1
]}

机构：

[1] Nanjing Univ Sci & Technol, Dept Appl Math, Nanjing 210094, Jiangsu, Peoples R China

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2013年 / 43卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Vectorial Sturm-Liouville problem; eigenvalue asymptotics; trace formula; inverse spectral problem; VALUED SCHRODINGER-OPERATORS; M-FUNCTION ASYMPTOTICS; BORG-TYPE THEOREMS; HILLS EQUATION; SPECTRUM;

D O I：

10.1216/RMJ-2013-43-6-2049

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper describes the N-dimensional vectorial Sturm-Liouville problem with coupled boundary conditions. We first derive the asymptotic expressions of large eigenvalues for the vectorial Sturm-Liouville operator with smooth coefficients. In addition, the regularized trace formula for the operator is calculated with residue techniques in complex analysis. These formulae are then used to obtain some results of inverse eigenvalue problems in the spirit of Ambarzumyan.

引用

页码：2049 / 2078

页数：30

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