一般边界条件下Sturm-Liouville算子的Ambarzumyan型定理

数学物理学报 ›› 2010, Vol. 30 ›› Issue (2): 449-455.

一般边界条件下Sturm-Liouville算子的Ambarzumyan型定理

杨传富, 杨孝平

南京理工大学应用数学系|南京 210094

收稿日期:2008-05-08 修回日期:2009-03-04 出版日期:2010-04-25 发布日期:2010-04-25
基金资助:
南京理工大学科研发展基金(AB96240)和国家自然科学基金(10771102/A0108)资助.

Ambarzumyan's Theorems for Sturm-Liouville Operators with General Boundary Conditions

YANG Chuan-Fu, YANG Xiao-Ping

Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094

Received:2008-05-08 Revised:2009-03-04 Online:2010-04-25 Published:2010-04-25
Supported by:
南京理工大学科研发展基金(AB96240)和国家自然科学基金(10771102/A0108)资助.

摘要/Abstract

摘要：

该文研究有限区间上一般自伴边界条件下的Sturm-Liouville方程的逆特征值问题.将Neumann边界条件下Sturm-Liouville方程的Ambarzumyan型定理推广到一般自伴边界条件下情形, 证明了如果它的特征值与零势的特征值一样,
则Sturm-Liouville方程的势为零.

关键词: Ambarzumyan型定理, 逆谱理论, 特征值渐近性, Rayleigh商原理

Abstract:

This paper deals with the inverse eigenvalue problems for the Sturm-Liouville equation on finite interval with general self-adjoint boundary conditions. The authors extend the classical Ambarzumyan's theorem for the Sturm-Liouville equation with Neumann boundary conditions to the general self-adjoint boundary conditions. They prove that if the spectrum is the same as the spectrum belonging to the zero potential and the potential possesses an integral condition, then the potential is actually zero.

Key words: Ambarzumyans theorem, Inverse spectral theory, Eigenvalue asymptotics, Rayleigh quotient

中图分类号:

34A55

杨传富, 杨孝平. 一般边界条件下Sturm-Liouville算子的Ambarzumyan型定理[J]. 数学物理学报, 2010, 30(2): 449-455.

YANG Chuan-Fu, YANG Xiao-Ping. Ambarzumyan's Theorems for Sturm-Liouville Operators with General Boundary Conditions[J]. Acta mathematica scientia,Series A, 2010, 30(2): 449-455.

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