一类华罗庚域的Bergman核函数的显式表达

Explicit Formulas of the Bergman Kernel Functions for A Class of Hua Domains

摘要: 在任意不可约有界圆型齐性域上考虑一类华罗庚域E(q₁, …, q_m, Ω; p₁, …, p_m)，其中Ω是指任意不可约有界圆型齐性域，q₁, …, q_m都是自然数，m, p₁, …, p_m都是正整数，N(Z, Z)是Ω的一般范数。利用完备正交函数系和多元极坐标变换，给出了该域的Bergman核函数的显式表达。

Abstract: Consider a class of Hua domains E(q₁, …, q_m, Ω; p₁, …, p_m) on any irreducible bounded circular homogeneity domain, and among them, Ω is any irreducible bounded circular homogeneity domain, q₁, …, q_m are all natural numbers, m, p₁, …, p_m are all positive integers, N(Z, Z) is the norm of Ω. The explicit formulas of the Bergman kernel functions for the domains are provided by using the complete orthogonal function system and multivariate polar coordinate transformation.