The heat equation on compact Lie group
The heat equation on compact Lie group
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紧致李群上的热方程
DOI：
10.18910/7850
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发表时间：
1975
影响因子：
0.4
通讯作者：
H. Urakawa
中科院分区：
文献类型：
--
作者：
H. Urakawa
McKean和Singer [9]提出了一个问题，即对于平坦环面以外的流形，存在类似的泊松求和公式。Y. Colin de Verdiere [3]在具有负截面曲率的二维紧致黎曼流形的情形下给出了一个答案。本文的目的是确定与热方程有关的Minakshisundaram展开式（定理3），并给出该方程基本解在单连通紧致半单李群上的Poisson求和公式（定理2）的类似形式。作者对K.冈本谁建议他研究泊松公式时，他获得定理3。
McKean and Singer [9] posed the problem of the existence of an analogue of the Poisson's summation formula for manifolds other than flat tori. Y. Colin de Verdiere [3] gave an answer to it in the case of a 2-dimensional compact Riemannian manifold with negative sectional curvature. The purpose of this paper is to determine the Minakshisundaram's expansion (Theorem 3) related to the heat equation and to give an analogue of the Poisson's summation formula of the fundamental solution of this equation on a simply-connected compact semi-simple Lie group (Theorem 2). The author expresses his gratitude to Prof. K. Okamoto who suggested him to study the Poisson's formula when he obtained Theorem 3.