数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (3): 480-492.doi: 10.1016/S0252-9602(09)60048-5
陆启铿
Lu Qikeng
摘要：
Two points of the infinite dimensional complex projective space CP∞ with homogeneous coordinates α=(α0, α1, α2, … ) and b=b0, b1, b2, … ), respectively, are conjugate if and only if they are complex orthogonal, i.e., αb = Σ∞j=0
αj bj =0. For a complete ortho-normal system φ(t)=(φ0(t), φ1(t), φ2(t), … ) of L2H(D), the space of the holomorphic and absolutely square integrable functions in the bounded domain D of Cn, φ(t), t ∈ D, is considered as the homogeneous coordinate of a point in CP∞. The correspondence t → φ(t) induces a holomorphic imbedding tφ : D → CP∞. It is proved that the Bergman kernel K(t, v) of D equals to zero for the two points t and v in D if and only if their image points under tφ are conjugate points of CP∞.
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