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

共 50 条

[21] The trace formula for Sturm-Liouville operator with operator coefficient
Adigüzelov, E
Avci, H
Gül, E
JOURNAL OF MATHEMATICAL PHYSICS, 2001, 42 (06) : 2611 - 2624
[22] Multiplicity of Sturm-Liouville eigenvalues
Kong, Q
Wu, H
Zettl, A
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 171 (1-2) : 291 - 309
[23] BOUNDS AND HIGHER-ORDER ESTIMATES FOR STURM-LIOUVILLE EIGENVALUES
PAINE, JW
ANDREW, AL
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1983, 96 (02) : 388 - 394
[24] Two inverse eigenvalue problems for vectorial Sturm-Liouville equations
Inverse Probl, 5 (1331-1343):
[25] Some inverse spectral problems for vectorial Sturm-Liouville equations
Shen, CL
INVERSE PROBLEMS, 2001, 17 (05) : 1253 - 1294
[26] Two inverse eigenvalue problems for vectorial Sturm-Liouville equations
Shen, CL
Shieh, CT
INVERSE PROBLEMS, 1998, 14 (05) : 1331 - 1343
[27] Distribution of eigenvalues and trace formula for the Sturm–Liouville operator equation
M. Bairamogly
N. M. Aslanova
Ukrainian Mathematical Journal, 2010, 62 : 1005 - 1017
[28] THE FORMULA FOR THE REGULARIZED TRACE OF THE STURM-LIOUVILLE OPERATOR WITH A LOGARITHMIC POTENTIAL
Ishkin, Khabir Kabirovich
Valiullina, Leisan Gabdullovna
TAMKANG JOURNAL OF MATHEMATICS, 2019, 50 (03): : 269 - 280
[29] A trace formula for the vector Sturm-Liouville operator with a constant delay
Dan, Li
Yang, Chuan-fu
APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B, 2025, 40 (01) : 213 - 222
[30] A trace formula for the vector Sturm-Liouville operator with a constant delay
LI Dan
YANG Chuan-fu
Applied Mathematics:A Journal of Chinese Universities, 2025, 40 (01) : 213 - 222

← 1 2 3 4 5 →