第二类华罗庚域的Bergman核函数的计算——纪念华罗庚90岁寿辰

The Computation of Bergman Kernel on Hua Domain of the Second Type

显式获得了第二类华罗庚域的 Bergman核函数 .第二类华罗庚域是指由如下表达式所界定的域 | w1| 2 p1+ | w2 | 2 p2 +… + | wn| 2 pn <det(I - ZZ)这里 ,1/ p1,1/ p2 ,… ,1/ pn-1都是正整数 ,pn 是任意正实数 ,RII(p )是第二类典型域 ,Z∈ RII(p) .关键之处有两点 :1)给出了将此域的任一内点 (W,Z)映为 (W*,0 )的全纯自同构群 ;2 )引进了 semi-Reinhardt域并给出了它的完备规范正交函数系 .

The authous get the Bergman kernel in explicit formula for the Hua domain of the second type defined by the following inequality: |w_1|^(2p_1)+|w_2|^(2p_2)+...+|w_n|^(2p_n)<det(I-Z) where, 1/p_1,1/p_2,...,1/p_(n-1) are positive integers, p_n is any positive real number, R_(II)(p) is the classical domain of the second type, Z∈R_(II)(p). There are two key steps: firstly authors get the holomorphic automorphism group for such Hua domain such that the each element of this group maps the inner points (W,Z_0) onto (W~*,0); secondly authors introduce the notion of semi-Reinhardt domain and get its complete orthonormal system.