| 微分算子的特征值与特征函数的Dirichlet级数和渐近分布 |
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| 引用本文： | 罗海生.微分算子的特征值与特征函数的Dirichlet级数和渐近分布[J].首都师范大学学报(自然科学版),1988(1). |
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| 作者姓名： | 罗海生 |
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| 作者单位： | 北京师范学院数学系 |
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| 摘 要： | 本文把Minakshisundaram关于Laplace算子特征值与特征函数的性质推广到一般情形,即对闭流形上半正定自伴椭圆型微分算子,证明了其特征值与特征函数决定的Dirichlet级数的收敛性和解析开拓,给出其特征值与特征函数的渐近分布。
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| 关 键 词： | 微分算子 特征值 特征函数 Dirichlet级数 渐近分布 |
Dirichlet's Series and Asymtotic Distribution of the Eigenvalues and Eigenfunctions of a Differential Operator |
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| Luo Haisheng.Dirichlet''''s Series and Asymtotic Distribution of the Eigenvalues and Eigenfunctions of a Differential Operator[J].Journal of Capital Normal University(Natural Science Edition),1988(1). |
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| Authors: | Luo Haisheng |
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| Institution: | Luo Haisheng |
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| Abstract: | In this paper, we extend results appeared in Minakshisundaram 3,4] to more general cases. That is, for a differential operator which is positive semi-definite (or of positive definite leading symbol), self-adjoint and elliptic on a closed manifold, we prove the convergence and continuation of the Dirichlet's series determined by the eigenvalues and eigenfunctions and give the asymtotic distribution of the eigenvalues and eigenfunctions. |
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| Keywords: | differential operator eigenvalue eigenfunction Dirichlet's series asymtotic distribution |
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