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

doi:10.1007/s11425-010-3125-5

	Poisson kernel and Cauchy formula of a non-symmetric transitive domain
	Lu Qi-Keng
刊名	SCIENCE CHINA-MATHEMATICS
	2010-07-01
卷号	53 期号:7 页码:1679-1684
关键词	Poisson kernel Cauchy formula
ISSN号	1674-7283
DOI	10.1007/s11425-010-3125-5
英文摘要	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.
语种	英语
出版者	SCIENCE PRESS
WOS记录号	WOS:000279713200002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/10542]
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.