某些华罗庚域的Bergman核函数的显式表达

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详细信息

Explicit formulas of the Bergman kernel functions for some domains of Hua Luo-Geng

摘要: 通过构造超几何函数和球型积分变换方法，给出了更多变量的新域 $E(k,q_{2},\cdots,q_{m}, \Omega,p_{2},\cdots,p_{m}$ 上的Bergman核函数的显示表达式,其中 $\Omega$ 是指任意不可约有界圆型齐性域， $k,m,q_{2},\cdots,q_{m}$ 都是正整数, $p_{2},\cdots,p_{m}$ 都是正实数， $N(Z,Z)$ 是 $\Omega$ 的一般范数.而且，当 $\Omega$ 是4大类的不可约的对称典型域时，上述域就是华罗庚域.同时可以得出相应华罗庚域上的Bergman核函数的显示表达式.
- 超几何函数
Abstract: The explicit formulas of the Bergman kernel functions for some new domains of Hua Luo-Geng are provided by constructing hypergeometric function and spherical integral transform method. Among them, $\Omega$ is any irreducible bounded circular homogeneity domain, $k,m,q_{2},\cdots,q_{m}$ are all positive integers, $p_{2},\cdots,p_{m}$ are all positive number, $N(Z, Z)$ is the norm of $\Omega$ .And when $\Omega$ is four categories of irreducible symmetrical typical domain, then the domain is Hua Luo-Geng domain. And the explicit formulas of the Bergman kernel functions for corresponding domains of Hua Luo-Geng can be drawn.
- hypergeometric function.