| THE COMPLETENESS OF EIGENFUNCTIONS OF PERTURBATION CONNECTED WITH STURM-LIOUVILLE OPERATORS |
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| 引用本文： | Zhong WANG Hongyou WU. THE COMPLETENESS OF EIGENFUNCTIONS OF PERTURBATION CONNECTED WITH STURM-LIOUVILLE OPERATORS[J]. 系统科学与复杂性, 2006, 19(4): 527-537. DOI: 10.1007/s11424-006-0527-0 |
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| 作者姓名： | Zhong WANG Hongyou WU |
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| 作者单位： | [1]Department of Mathematics, Zhaoqing University, Zhaoqing 526061, China. [2]Department of Mathematics, Northern Illinois University, DEKA LB, Illinois 60115-2854, USA. |
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| 基金项目： | The author is partially supported by the Nature Science Foundation of Guangdong （5012285）, the ＂Thousand, Hundred, Ten＂ Science Foundation of Guangdong （Q02052）, the Nature Science Foundation of Education Bureau of Guangdong （Z02075）. |
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| 摘 要： | In this paper, non-self-adjoint Sturm-Liuville operators in Weyl＇s limit-circle case are studied. We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-Liouville differential expression. Then, using the characteristic determinant, we prove the completeness of the system of eigenfunctions and associated functions for these dissipative operators.
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| 关 键 词： | 算子 非自伴随矩阵 边界条件 弯曲消耗算子 |
| 收稿时间： | 2004-06-08 |
| 修稿时间： | 2004-06-082005-10-06 |
The Completeness of Eigenfunctions of Perturbation Connected with Sturm-Liouville Operators |
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| Zhong Wang,Hongyou Wu. The Completeness of Eigenfunctions of Perturbation Connected with Sturm-Liouville Operators[J]. Journal of Systems Science and Complexity, 2006, 19(4): 527-537. DOI: 10.1007/s11424-006-0527-0 |
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| Authors: | Zhong Wang Hongyou Wu |
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| Affiliation: | (1) Department of Mathematics, Zhaoqing University, Zhaoqing, 526061, China;(2) Department of Mathematics, Northern Illinois University, DEKALB, Illinois, 60115-2854, USA |
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| Abstract: | In this paper,non-self-adjoint Sturm-Liuville operators in Weyl's limit-circle case are stud- ied.We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-Liouville differential expression.Then,using the characteristic determinant,we prove the completeness of the system of eigenfunctions and associated functions for these dissipative operators. |
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| Keywords: | Characteristic determinant completeness dissipative operators eigenfunctions Sturm- Liouville differential operators. |
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