The Parametric Representation Of Holomorphic Mapping And Roper-Suffridge Operator

Roper-Suffridge operator is introduced,which connects geometric function theory of simple complex variables and several complex variables theory,and plays an important role in constructing biholomorphic mappings from biholomorphic functions,in this paper,the properties of Roper-Suffridge operator are generalized,that is,the properties of Roper-Suffridge operator on Bn in Cn and bounded complete Reinhardt domain Bp are generalized,the paper is divided into three chapters.In the first chapter,we describe the research background,symbols,definitions,the-orems and main theorems in this paper;In the second chapter,according to the parameter representation of star map and screw map,a new kind of Roper-Suffridge operator is given,this operator can generate the spiral map on unit ball Bn and Reinhardt domain ?;In the third chapter,parametric representation based on screw mapping,prove this kind of Roper-Suffridge operator,keep screw shape on Reinhardt domain Bp and Reinhardt domain ?;The result of this paper can be said to be the application of holomorphic mapping parameters,and it is also a further study and generalization of the previous work,got some brand-new content,it is also a deep understanding of the Roper-Sufffridge operator,and the results of this paper enrich the content of several complex variables.