![Sample our Computer Science journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5928/TOC-Subject-Sample-2021-Computer-Science.jpg"})
Abstract
In this article we consider the Schwarz problem for holomorphic functions in the Siegel domain D, the boundary of which is the Heisenberg group H. We first prove the Cauchy–Szegö formula for D by using the same formula for the unit ball. Then the Plemelj formula for H is proved. At last, we get solvability conditions for the Schwarz problem, and under these conditions its general solution is given by an explicit formula.
Acknowledgements
L. Hua is in debt to the DAAD-K.C.Wong foundation for supporting his visit research in 2007/2008 at FU Berlin. He is also grateful to Professor H. Begehr for his many helpful comments This research was supported by NSF of China No.10601036 and NSF of Tianjin Municipal No. 07JCYBJC13600.