Poisson kernel and Cauchy formula of a non-symmetric transitive domain

doi:10.1007/s11425-010-3125-5

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	Poisson kernel and Cauchy formula of a non-symmetric transitive domain
	Lu Qi-Keng
	2010-07-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	53 期号:7 页码:1679-1684
摘要	In 1965, Lu Yu-Qian discovered that the Poisson kernel of the homogenous domain S(m,p,q) = {Z is an element of C(mxm), Z(1) is an element of C(mxp), Z(2) is an element of C(qxm)\|1/2i(Z-Z(dagger))-Z(1)(Z) over bar'(1) - (Z) over bar'(2) > 0} does not satisfy the Laplace-Beltrami equation associated with the Bergman metric when S(m,p,q) is not symmetric. However the map T(0) : Z -> Z, Z(1)-> Z(1), Z(2)-> Z(2) transforms S(m,p,q) into a domain S(I) (m, m+p+q) which can be mapped by the Cayley transformation into the classical domains R(I) (m,m + p + q). The pull back of the Bergman metric of R(I) (m,m + p + q) to S(m,p,q) is a Riemann metric ds(2) which is not a Kahler metric and even not a Hermitian metric in general. It is proved that the Laplace-Beltrami operator Delta associated with the metric ds(2) when it acts on the Poisson kernel of S(m,p,q) equals 0. Consequently, the Cauchy formula of S(m,p,q) can be obtained from the Poisson formula.
关键词	Poisson kernel Cauchy formula
DOI	10.1007/s11425-010-3125-5
语种	英语
资助项目	National Natural Science Foundation of China[10671194] ; National Natural Science Foundation of China[10731080/A01010501]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000279713200002
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10543
专题	中国科学院数学与系统科学研究院
通讯作者	Lu Qi-Keng
作者单位	Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Lu Qi-Keng. Poisson kernel and Cauchy formula of a non-symmetric transitive domain[J]. SCIENCE CHINA-MATHEMATICS,2010,53(7):1679-1684.
APA	Lu Qi-Keng.(2010).Poisson kernel and Cauchy formula of a non-symmetric transitive domain.SCIENCE CHINA-MATHEMATICS,53(7),1679-1684.
MLA	Lu Qi-Keng."Poisson kernel and Cauchy formula of a non-symmetric transitive domain".SCIENCE CHINA-MATHEMATICS 53.7(2010):1679-1684.