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 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 Sharp estimates of approximation of classes of differentiable functions by entire functions

2021 ◽  
pp. 3
Author(s):  
V.F. Babenko ◽  
A.Yu. Gromov
Keyword(s):  
Exponential Type ◽  
Best Approximation ◽  
Entire Functions ◽  
Sharp Estimate ◽  
Sharp Estimates ◽  
The Best Approximation ◽  
Differentiable Functions ◽  
Functions Of Exponential Type

In the paper, we find the sharp estimate of the best approximation, by entire functions of exponential type not greater than $\sigma$, for functions $f(x)$ from the class $W^r H^{\omega}$ such that $\lim\limits_{x \rightarrow -\infty} f(x) = \lim\limits_{x \rightarrow \infty} f(x) = 0$,$$A_{\sigma}(W^r H^{\omega}_0)_C = \frac{1}{\sigma^{r+1}} \int\limits_0^{\pi} \Phi_{\pi, r}(t)\omega'(t/\sigma)dt$$for $\sigma > 0$, $r = 1, 2, 3, \ldots$ and concave modulus of continuity.Also, we calculate the supremum$$\sup\limits_{\substack{f\in L^{(r)}\\f \ne const}} \frac{\sigma^r A_{\sigma}(f)_L}{\omega (f^{(r)}, \pi/\sigma)_L} = \frac{K_L}{2}$$

scholarly journals Meansquare Approximation of Function Classes, Given on the all Real Axis R by the Entire Functions of Exponential Type

2016 ◽  
Vol 6 ◽  
pp. 1-12 ◽  
Author(s):  
Sergey B. Vakarchuk
Keyword(s):  
Exponential Type ◽  
Best Approximation ◽  
Fractional Derivatives ◽  
Entire Functions ◽  
Weak Equivalence ◽  
The Best Approximation ◽  
Function Classes ◽  
Functions Of Exponential Type ◽  
Specific Restriction ◽  
Derivatives Of

K-functionals K (f, t, L2(R), L2β(R), which defined by the fractional derivatives of order β>0, have been considered in the space L2(R). The relation K (f, tβ, L2(R), L2β(R) ≈ ωβ (f, t) (t>0) was obtained in the sense of the weak equivalence, where ωωβ (f, t) is the module of continuity of the fractional order β for a function f є L2(R). Exact values of the best approximation by entire functions of exponential type v∏, v є (0, ∞) have been computed for the classes of functions, given by the indicated K-functionals and majorants Ψ satisfying specific restriction. Kolmogorov, Bernsteinand linear mean v-widths were obtained for indicated classes of functions.

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