Generalized growth and best approximation of entire functions in L p -norm in several complex variables

2011 ◽  
Vol 57 (2) ◽  
pp. 353-372 ◽  
Author(s):  
Devendra Kumar
Keyword(s):  
Best Approximation ◽  
Entire Functions ◽  
Complex Variables ◽  
Several Complex Variables

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 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.

scholarly journals Gol'dberg Order and Gol'dberg Type of Entire Functions Represented by Multiple Dirichlet Series

1970 ◽  
Vol 29 ◽  
pp. 63-70
Author(s):  
Md Feruj Alam
Keyword(s):  
Dirichlet Series ◽  
Hadamard Product ◽  
Entire Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Multiple Dirichlet Series

We consider the Hadamard product of the class of entire multiple Dirichlet series in several complex variables having the same sequence of exponents. Our object is to study the nature of Gol'dberg order and Gol’dberg type of these functions. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 29 (2009) 63-70  DOI: http://dx.doi.org/10.3329/ganit.v29i0.8516

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