Poisson kernel and Cauchy formula of a non-symmetric transitive domain
文献类型：期刊论文
| 作者 | Lu Qi-Keng |
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000279713200002 |
| 出版者 | SCIENCE PRESS |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。