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| 高阶加权微分算子谱的离散性 | |
| 引用本文： | 张茂柱,孙炯,敖继军.高阶加权微分算子谱的离散性[J].数学杂志,2012,32(2):331-338. |
| 作者姓名： | 张茂柱 孙炯 敖继军 |
| 作者单位： | 1. 内蒙古大学数学科学学院,内蒙古呼和浩特010021;泰山学院数学与系统科学学院,山东泰安271021 2. 内蒙古大学数学科学学院,内蒙古呼和浩特,010021 3. 内蒙古大学数学科学学院,内蒙古呼和浩特010021;内蒙古工业大学理学院,内蒙古呼和浩特010051 |
| 基金项目： | 国家自然科学基金资助项目 |
| 摘 要： | 本文研究了加权的高阶微分算子的谱. 利用分解的方法和不等式的估计, 得到了一些高阶对称微分算子的任何自共轭扩张的谱离散的充分条件, 推广了 Pfeiffer , Sun, Glazman 等人的结果,利用这些结果可以判别某些微分算子谱的离散性. |
| 关 键 词： | 微分算子 离散谱 权函数 |
DISCRETENESS OF SPECTRA OF HIGH ORDER DIFFERENTIAL OPERATORS WITH WEIGHTED FUNCTIONS |
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| ZHANG Mao-zhu , SUN Jiong , AO Ji-jun.DISCRETENESS OF SPECTRA OF HIGH ORDER DIFFERENTIAL OPERATORS WITH WEIGHTED FUNCTIONS[J].Journal of Mathematics,2012,32(2):331-338. | |
| Authors: | ZHANG Mao-zhu SUN Jiong AO Ji-jun |
| Institution: | 1,3(1.School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)(2.College of Mathematics and System Science,Taishan University,Taian 271021,China)(3.College of Sciences,Inner Mongolia University of Technology,Hohhot 010051,China) |
| Abstract: | The investigations deal with the spectra of high order differential operators with weighted functions.Using the method of decomposition and the estimate of inequalities,we obtain the spectra of all the self-adjoint extensions of high order symmetric differential operators are discrete under certain conditions on the coefficients.Our results extend the results of Mller Pfeiffer E.,Sun Jiong and Glazman.Using the results obtained,we can easily judge the discreteness of spectra of some differential operators. |
| Keywords: | differential operators discrete spectrum weighted functions |
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