关于多复变数的全纯支撑函数和单位分解

ON HOLOMORPHIC SUPPORT FUNCTION AND PARTITION OF UNITY IN SEVERAL COMPLEX VARIABLES

对Ｃ￣ｎ空间中的任何有界域，证明都不具有关于ζ∈ 和Ｚ∈ 全纯的支撑函数ψ（ζ，ｚ）和相应的单位分解。它揭示了多复变数与单复变数哥西核函数的一个最本质的区别：对Ｃ￣ｍ中的任何有界域上都不存在类似单复变数关于ζ∈ 和Ｚ∈ 全纯的哥西核函数，这也是多复变数积分表示理论中的一个本质问题。

For a bounded domain D in space C￣n,we prove that the domain does not admit anyholomorphic support function and corresponding partition of unity.These results reveal essentialdiffernces bet ween the cauchy kernel fu nctions in several complex varables and single complexvariable; that is, in several complex there does not possese any Cauchy kernel function which isholomorphic in ξ∈D and in z∈D as in the case of single variable.