Abstract
This paper introduces the Hua construction and presents the holomorphic automorphism group of the Hua construction of the fourth type. Utilizing the Bergman kernel function, under the condition of holomorphic automorphism and the standard complete orthonormal system of the semi-Reinhardt domain, the infinite series from of the Bergman kernel function is derived. By applying the properties of polynomial and Γ functions, various identification relations of the aforementioned form are developed and the explicit formula of the Bergman kernel function for the Hua construction of the fourth type is obtained, which suggest that many of the previously-reported results are only the special cases of our findings.
*Supported by Natural Science Foundation of China (Grant No. 10471097) and the Doctor Station Foundation of the Ministry of Education
Notes
*Supported by Natural Science Foundation of China (Grant No. 10471097) and the Doctor Station Foundation of the Ministry of Education