| Euler微分算子谱是离散的充分必要条件 |
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| 引用本文： | 王忠,孙炯.Euler微分算子谱是离散的充分必要条件[J].系统科学与数学,2001,21(4):497-506. |
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| 作者姓名： | 王忠 孙炯 |
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| 作者单位： | 1. 肇庆学院数学系,广东肇庆526061
2. 内蒙古大学数学系,呼和浩特010021 |
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| 基金项目： | 国家自然科学基金(1987037)资助课题. |
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| 摘 要： | 本文在研究一类高阶微分算子谱的离散性的基础上研究了2n阶实系数Euler微分算式生成的对称微分算子,进一步完善了自伴Euler微分算子的谱是离散的充分必要条件.
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| 关 键 词： | Euler微分算式 微分算子 离散谱 本质谱. |
| 修稿时间： | 2000年10月23 |
SUFFICIENT AND NECESSARY CONDITIONS FOR DISCRETENESS OF SPECTRUM OF EULER DIFFERENTIAL OPERATORS |
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| Zhong Wang,Jiong SUN.SUFFICIENT AND NECESSARY CONDITIONS FOR DISCRETENESS OF SPECTRUM OF EULER DIFFERENTIAL OPERATORS[J].Journal of Systems Science and Mathematical Sciences,2001,21(4):497-506. |
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| Authors: | Zhong Wang Jiong SUN |
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| Institution: | (1)Department of Mathematics, Zhaoqing University, Guangdong Zhaoqing 526061,P.R.China;(2)Department of Mathematics, Inner Mongolia University, Huhehaote 010021,P.R.China |
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| Abstract: | In this paper, the 2nd order symmetric Euler differential expressions with real-valued coefficients are considered. Some results concerning the discreteness of spectrum of Euler differential operators is obtained. Especially, the necessary and sufficient conditions are given which ensure that the spectrum of Euler differential operators is discrete. |
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| Keywords: | Euler differential expression differential operator discrete spectrum essential spectrum |
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