On the theory of functions of several complex variables. I. A complete system of orthogonal functions in the hyperbolic space of matrices

1963 ◽  
pp. 163-194
Author(s):  
Hua Loo-Keng
Keyword(s):  
Hyperbolic Space ◽  
Complete System ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Orthogonal Functions

scholarly journals Meromorphic or Holomorphic Completion of a Reinhardt Domain

1970 ◽  
Vol 38 ◽  
pp. 1-12 ◽  
Author(s):  
Eiichi Sakai
Keyword(s):  
Meromorphic Function ◽  
Power Series ◽  
Meromorphic Functions ◽  
Integral Formula ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Reinhardt Domain ◽  
Continuity Theorem ◽  
Cauchy’S Integral Formula ◽  
Long Time

In the theory of functions of several complex variables, the problem about the continuation of meromorphic functions has not been much investigated for a long time in spite of its importance except the deeper result of the continuity theorem due to E. E. Levi [4] and H. Kneser [3], The difficulty of its investigation is based on the following reasons: we can not use the tools of not only Cauchy’s integral formula but also the power series and there are indetermination points for the meromorphic function of many variables different from one variable. Therefore we shall also follow the Levi and Kneser’s method and seek for the aspect of meromorphic completion of a Reinhardt domain in Cn.

scholarly journals Geometric Mappings under the Perturbed Extension Operators in Complex Systems Analysis

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Chaojun Wang ◽  
Yanyan Cui ◽  
Hao Liu
Keyword(s):  
Complex Systems ◽  
Unit Ball ◽  
Systems Analysis ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Geometric Properties ◽  
Geometric Characteristics ◽  
New Approaches ◽  
Special Cases ◽  
Hartogs Domains

In this paper, we mainly seek conditions on which the geometric properties of subclasses of biholomorphic mappings remain unchanged under the perturbed Roper-Suffridge extension operators. Firstly we generalize the Roper-Suffridge operator on Bergman-Hartogs domains. Secondly, applying the analytical characteristics and growth results of subclasses of biholomorphic mappings, we conclude that the generalized Roper-Suffridge operators preserve the geometric properties of strong and almost spiral-like mappings of typeβand orderα,SΩ⁎(β,A,B)as well as almost spiral-like mappings of typeβand orderαunder different conditions on Bergman-Hartogs domains. Sequentially we obtain the conclusions on the unit ballBnand for some special cases. The conclusions include and promote some known results and provide new approaches to construct biholomorphic mappings which have special geometric characteristics in several complex variables.

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