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 .

scholarly journals Best Polynomial Approximation in -Norm and -Growth of Entire Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed El Kadiri ◽  
Mohammed Harfaoui
Keyword(s):  
Continuous Function ◽  
Polynomial Approximation ◽  
Extremal Function ◽  
Entire Functions ◽  
Maximum Norm ◽  
Best Polynomial Approximation ◽  
General Growth ◽  
Growth Of Entire Functions ◽  
Approximation Errors ◽  
Positive Capacity

The classical growth has been characterized in terms of approximation errors for a continuous function on by Reddy (1970), and a compact of positive capacity by Nguyen (1982) and Winiarski (1970) with respect to the maximum norm. The aim of this paper is to give the general growth (-growth) of entire functions in by means of the best polynomial approximation in terms of -norm, with respect to the set , where is the Siciak's extremal function on an -regular nonpluripolar compact is not pluripolar.

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 On the growth of system of entire homogenous polynomials of several complex variables

2016 ◽  
Vol 11 (9) ◽  
pp. 5674-5679
Author(s):  
Aseel Hameed ◽  
MushtaqShakir A.Hussein
Keyword(s):  
Entire Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Growth Of Entire Functions ◽  
Order And Type

In this paper we study the growth of entire functions represented by homogenous polynomials of two complex variables. The characterizations of their order and type have been obtained

scholarly journals Mean-periodic functions

1980 ◽  
Vol 3 (2) ◽  
pp. 199-235 ◽  
Author(s):  
Carlos A. Berenstein ◽  
B. A. Taylor
Keyword(s):  
Partial Differential Equations ◽  
Periodic Function ◽  
Entire Functions ◽  
Convolution Equation ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Exponential Polynomial ◽  
Periodic Functions ◽  
Open Questions ◽  
Constant Coefficients

We show that any mean-periodic functionfcan be represented in terms of exponential-polynomial solutions of the same convolution equationfsatisfies, i.e.,u∗f=0(μ∈E′(ℝn)). This extends ton-variables the work ofL. Schwartz on mean-periodicity and also extendsL. Ehrenpreis' work on partial differential equations with constant coefficients to arbitrary convolutors. We also answer a number of open questions about mean-periodic functions of one variable. The basic ingredient is our work on interpolation by entire functions in one and several complex variables.

scholarly journals ON CERTAIN SUB-SPACE OF X

2008 ◽  
Vol 5 (4) ◽  
pp. 660-668
Author(s):  
Baghdad Science Journal
Keyword(s):  
Entire Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Topological Properties

The study of properties of space of entire functions of several complex variables was initiated by Kamthan [4] using the topological properties of the space. We have introduced in this paper the sub-space of space of entire functions of several complex variables which is studied by Kamthan.

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