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

	THE CONJUGATE POINTS OF CP infinity AND THE ZEROES OF BERGMAN KERNEL
	Lu Qikeng
刊名	ACTA MATHEMATICA SCIENTIA
	2009-05-01
卷号	29 期号:3 页码:480-492
关键词	conjugate points Bergman kernel
ISSN号	0252-9602
英文摘要	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.
语种	英语
出版者	ELSEVIER SCIENCE INC
WOS记录号	WOS:000265911500003
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/8581]
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.