Sharpness Almost Everywhere of Equivalence Assertions for the Best Approximation by Algebraic Polynomials

1996 ◽  
Vol 28 (4) ◽  
pp. 367-372
Author(s):  
L. Imhof ◽  
R. J. Nessel
Keyword(s):  
Best Approximation ◽  
Algebraic Polynomials ◽  
The Best Approximation ◽  
Almost Everywhere ◽  
Approximation By Algebraic Polynomials

NOTE ON JACKSON AND BERNSTE N TYPE APPROXIMATION THEOREMS IN THE CASE OF APPROXIMATION BY ALGEBRAIC POLYNOMIALS N THE SPACES L AND C

2000 ◽  
Vol 36 (3-4) ◽  
pp. 353-358 ◽  
Author(s):  
S. Pawelke
Keyword(s):  
Periodic Function ◽  
Best Approximation ◽  
Trigonometric Polynomials ◽  
Algebraic Polynomials ◽  
Cient Condition ◽  
Approximation Theorems ◽  
Type Approximation ◽  
The Best Approximation ◽  
Approximation By Algebraic Polynomials

We con ider the best approximation E (n,f)by algebraic polynomials of degree at most n for function f in L 1 (-1, 1)or C [-1, 1]and give imple necessary and u .cient condition for E (n,f)=O (n-.),n ›.,u ing the well-known results in the ca e of ap- proximation of periodic function by trigonometric polynomials.

scholarly journals Sharp inequalities of Jackson type in weighted space $L_{2;\rho}({\mathbb{R}}^2)$

2014 ◽  
Vol 22 ◽  
pp. 17
Author(s):  
S.B. Vakarchuk ◽  
M.B. Vakarchuk
Keyword(s):  
Best Approximation ◽  
Weighted Space ◽  
Jackson Type ◽  
Algebraic Polynomials ◽  
The Best Approximation ◽  
Differentiable Functions ◽  
Functions Of Two Variables

Sharp inequalities of Jackson type, connected with the best approximation by "angles" of algebraic polynomials have been obtained on the classes of differentiable functions of two variables in the metric of space $L_{2;\rho}({\mathbb{R}}^2)$ of the Chebyshev-Hermite weight.

scholarly journals The best approximation of classes $W^r H^{\omega}$ by algebraic polynomials in $L_1$ space

1998 ◽  
Vol 6 ◽  
pp. 52
Author(s):  
A.M. Kogan
Keyword(s):  
Asymptotic Behavior ◽  
Best Approximation ◽  
Algebraic Polynomials ◽  
The Best Approximation

We consider asymptotic behavior of the best approximation of classes $W^r H^{\omega}$ by algebraic polynomials in $L_1$ space.

scholarly journals On approximation of functions by algebraic polynomials on the average in real domain with Chebyshev-Hermite weight

2021 ◽  
Vol 19 ◽  
pp. 28
Author(s):  
S.B. Vakarchuk ◽  
M.B. Vakarchuk
Keyword(s):  
Best Approximation ◽  
Algebraic Polynomials ◽  
Approximation Of Functions ◽  
The Best Approximation ◽  
Real Domain

Exact inequalities of Jackson's type, connected with the best approximation of functions by algebraic polynomials, have been obtained in the space $L_{2,\rho}(\mathbb{R})$ at the Chebyshev-Hermite weight.

scholarly journals On the best approximation, by polynomials, of some classes of functions

1998 ◽  
Vol 6 ◽  
pp. 92
Author(s):  
O.V. Motornaia
Keyword(s):  
Best Approximation ◽  
Conjugate Functions ◽  
Algebraic Polynomials ◽  
Best Approximations ◽  
The Best Approximation ◽  
Approximation By Polynomials

We obtain asymptotically exact estimates of the best approximations of classes of conjugate functions by algebraic polynomials in the spaces $C$ and $L_1$.

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