The relation between the rate of growth of an entire function of several complex variables and the set of singular points of its associated function

1963 ◽  
pp. 315-322
Author(s):  
M. Š. Stavskiĭ
Keyword(s):  
Entire Function ◽  
Complex Variables ◽  
Singular Points ◽  
Several Complex Variables ◽  
Rate Of Growth ◽  
Associated Function

scholarly journals Generalized Order and Best Approximation of Entire Function in -Norm

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Mohammed Harfaoui
Keyword(s):  
Entire Function ◽  
Polynomial Approximation ◽  
Best Approximation ◽  
Extremal Function ◽  
Entire Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Best Polynomial Approximation ◽  
Growth Of Entire Functions

The aim of this paper is the characterization of the generalized growth of entire functions of several complex variables by means of the best polynomial approximation and interpolation on a compact with respect to the set , where is the Siciak extremal function of a -regular compact .

Growth Analysis of Composite Entire Functions of Several Complex Variables Based on Relative Order

2020 ◽  
pp. 151-163
Author(s):  
Balram Prajapati ◽  
Anupama Rastogi
Keyword(s):  
Entire Function ◽  
Lower Order ◽  
Growth Analysis ◽  
Entire Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Relative Order ◽  
Growth Properties

<p>In this paper we introduce some new results depending on the comparative growth properties of composition of entire function of several complex variables using relative L^*-order, Relative L^*-lower order and L≡L(r_1,r_2,r_3,……..,r_n) is a slowly changing functions. We prove some relation between relative L^*- order and relative L^*- lower order.</p>

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.

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