THE CONJUGATE POINTS OF CP infinity AND THE ZEROES OF BERGMAN KERNEL

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	THE CONJUGATE POINTS OF CP infinity AND THE ZEROES OF BERGMAN KERNEL
	Lu Qikeng
	2009-05-01
发表期刊	ACTA MATHEMATICA SCIENTIA
ISSN	0252-9602
卷号	29 期号:3 页码:480-492
摘要	Two points of the infinite dimensional complex projective space CP infinity with homogeneous coordinates a = (a(0), a(1), a(2), ...) and b = (b(0), b(1), b(2), ...) respectively, are conjugate if and only if they are complex orthogonal, i.e., ab(dagger) = (j=0)Sigma(infinity)a(j)(b) over bar (j) = 0. For a complete ortho-normal system phi(t) = (phi(0)(t), phi(1)(t), phi(2)(t), ...) of L-2 H(D), the space of the holomorphic and absolutely square integrable functions in the bounded domain D of C-n, phi(t), t is an element of D, is considered as the homogeneous coordinate of a point in CP infinity. The correspondence t -> phi(t) induces a holomorphic imbedding iota(phi) : D -> CP infinity. It is proved that the Bergman kernel K(t, (v) over bar) of D equals to zero for the two points t and v in D if and only if their image points under iota(phi) are conjugate points of CP infinity.
关键词	conjugate points Bergman kernel
语种	英语
资助项目	NSF of China[A01010501] ; NSF of China[10731080]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000265911500003
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8582
专题	中国科学院数学与系统科学研究院
通讯作者	Lu Qikeng
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 Qikeng. THE CONJUGATE POINTS OF CP infinity AND THE ZEROES OF BERGMAN KERNEL[J]. ACTA MATHEMATICA SCIENTIA,2009,29(3):480-492.
APA	Lu Qikeng.(2009).THE CONJUGATE POINTS OF CP infinity AND THE ZEROES OF BERGMAN KERNEL.ACTA MATHEMATICA SCIENTIA,29(3),480-492.
MLA	Lu Qikeng."THE CONJUGATE POINTS OF CP infinity AND THE ZEROES OF BERGMAN KERNEL".ACTA MATHEMATICA SCIENTIA 29.3(2009):480-492.