Generalized order and type of entire functions and best approximation in L p -norm

2012 ◽  
Vol 59 (2) ◽  
pp. 393-401
Author(s):  
G. S. Srivastava
Keyword(s):  
Best Approximation ◽  
Entire Functions ◽  
Order And Type ◽  
Generalized Order

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 On the Ritt order and type of a certain class of functions defined byBE-Dirichletian elements

1999 ◽  
Vol 22 (3) ◽  
pp. 445-458
Author(s):  
Marcel Berland
Keyword(s):  
Finite Number ◽  
Entire Functions ◽  
Number Of Zeros ◽  
Order And Type ◽  
Class Of Functions

We introduce the notions of Ritt order and type to functions defined by the series∑n=1∞fn(σ+iτ0)exp(−sλn),      s=σ+iτ,(σ,τ)∈R×R                                            (*)indexed byτ0onR, where(λn)1∞is aD-sequence and(fn)1∞is a sequence of entire functions of bounded index with at most a finite number of zeros. By definition, the series areBE-Dirichletian elements. The notions of order and type of functions, defined byB-Dirichletian elements, are considered in [3, 4]. In this paper, using a technique similar to that used by M. Blambert and M. Berland [6], we prove the same properties of Ritt order and type for these functions.

Growth and approximation of solutions to a class of certain linear partial differential equations in ℝN

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Devendra Kumar
Keyword(s):  
Symmetric Solution ◽  
Entire Functions ◽  
Polynomial Interpolation ◽  
Growth Parameters ◽  
Harmonic Polynomial ◽  
Axially Symmetric ◽  
Harmonic Polynomials ◽  
Linear Partial Differential Equations ◽  
Order And Type ◽  
Interpolation Polynomials

AbstractIn this paper we consider the equation ∇2 φ + A(r 2)X · ∇φ + C(r 2)φ = 0 for X ∈ ℝN whose coefficients are entire functions of the variable r = |X|. Corresponding to a specified axially symmetric solution φ and set C n of (n + 1) circles, an axially symmetric solution Λn*(x, η;C n) and Λn(x, η;C n) are found that interpolates to φ(x, η) on the C n and converges uniformly to φ(x, η) on certain axially symmetric domains. The main results are the characterization of growth parameters order and type in terms of axially symmetric harmonic polynomial approximation errors and Lagrange polynomial interpolation errors using the method developed in [MARDEN, M.: Axisymmetric harmonic interpolation polynomials in ℝN, Trans. Amer. Math. Soc. 196 (1974), 385–402] and [MARDEN, M.: Value distribution of harmonic polynomials in several real variables, Trans. Amer. math. Soc. 159 (1971), 137–154].

THE RATE OF BEST APPROXIMATION FOR ENTIRE FUNCTIONS

Analysis ◽  
1985 ◽  
Vol 5 (3) ◽  
Author(s):  
M. Freund ◽  
E. Görlich
Keyword(s):  
Best Approximation ◽  
Entire Functions

scholarly journals RELATIVE GROWTH OF ENTIRE DIRICHLET SERIES WITH DIFFERENT GENERALIZED ORDERS

2021 ◽  
Vol 9 (2) ◽  
pp. 22-34
Author(s):  
M. Sheremeta ◽  
O. Mulyava
Keyword(s):  
Dirichlet Series ◽  
Lower Order ◽  
Entire Functions ◽  
Entire Dirichlet Series ◽  
Relative Growth ◽  
Alpha Beta ◽  
Generalized Order

For entire functions $F$ and $G$ defined by Dirichlet series with exponents increasing to $+\infty$ formulas are found for the finding the generalized order $\displaystyle \varrho_{\alpha,\beta}[F]_G = \varlimsup\limits_{\sigma\to=\infty} \frac{\alpha(M^{-1}_G(M_F(\sigma)))}{\beta(\sigma)}$ and the generalized lower order $\displaystyle \lambda_{\alpha,\beta}[F]_G=\varliminf\limits_{\sigma\to+\infty} \frac{\alpha(M^{-1}_G(M_F(\sigma)))}{\beta(\sigma)}$ of $F$ with respect to $G$, where $M_F(\sigma)=\sup\{|F(\sigma+it)|:\,t\in{\Bbb R}\}$ and $\alpha$ and $\beta$ are positive increasing to $+\infty$ functions.

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