scholarly journals The best polynomial approximations of some classes of analytic functions in the Hardy spaces

2018 ◽  
Vol 26 (1) ◽  
pp. 8 ◽  
Author(s):  
S.B. Vakarchuk ◽  
V.I. Zabutna ◽  
M.B. Vakarchuk
Keyword(s):  
Polynomial Approximation ◽  
Hardy Spaces ◽  
Analytic Functions ◽  
Best Polynomial Approximation ◽  
Polynomial Approximations ◽  
Methods Of Approximation

Problems of the best polynomial approximation of classes of analytic functions $$$H^m_{p,R}$$$, $$$m\in \mathbb{Z}_+$$$, $$$R \geqslant 1$$$, $$$1 \leqslant p \leqslant \infty$$$, have been investigated in the Hardy spaces $$$H_p$$$. The best linear methods of approximation were constructed on the indicated classes.

scholarly journals On the best polynomial approximation of $(\psi,\beta)$-differentiable functions in $L_2$ space

2017 ◽  
Vol 25 ◽  
pp. 3
Author(s):  
S.B. Vakarchuk
Keyword(s):  
Modulus Of Continuity ◽  
Polynomial Approximation ◽  
Best Polynomial Approximation ◽  
Polynomial Approximations ◽  
Differentiable Functions ◽  
Beta 2

On the classes $L^{\psi}_{\beta,2}$ exact estimates have been obtained for the values of the best polynomial approximations of $(\psi,\beta)$-differentiable functions, expressed by the averages modulus of continuity $\widehat{\omega}(f^{\psi}_{\beta},t)$ with a weight $\xi(t)$. This modulus was introduced by K.V. Runovski and H.J. Schmeisser.

scholarly journals How much faster does the best polynomial approximation converge than Legendre projection?

2021 ◽  
Vol 147 (2) ◽  
pp. 481-503
Author(s):  
Haiyong Wang
Keyword(s):  
Polynomial Approximation ◽  
Best Polynomial Approximation

Some inequalities between the best polynomial approximation and averaged finite-difference norms in space L2

2021 ◽  
pp. 78-91
Author(s):  
Mirgand Shabozovich Shabozov ◽  
◽  
Munim Abdumamadovich Abdulkhaminov ◽  
Keyword(s):  
Finite Difference ◽  
Polynomial Approximation ◽  
Best Polynomial Approximation

scholarly journals Variable Exponent Spaces of Analytic Functions

2020 ◽  
Author(s):  
Gerardo A. Chacón ◽  
Gerardo R. Chacón
Keyword(s):  
Hardy Spaces ◽  
Measurable Function ◽  
Analytic Functions ◽  
Variable Exponent ◽  
Bergman Spaces ◽  
Lebesgue Spaces ◽  
Basic Properties ◽  
Variable Exponent Spaces ◽  
Real Functions ◽  
Spaces Of Analytic Functions

Variable exponent spaces are a generalization of Lebesgue spaces in which the exponent is a measurable function. Most of the research done in this topic has been situated under the context of real functions. In this work, we present two examples of variable exponent spaces of analytic functions: variable exponent Hardy spaces and variable exponent Bergman spaces. We will introduce the spaces together with some basic properties and the main techniques used in the context. We will show that in both cases, the boundedness of the evaluation functionals plays a key role in the theory. We also present a section of possible directions of research in this topic.

scholarly journals Polynomial Approximation of Anisotropic Analytic Functions of Several Variables

2020 ◽  
Author(s):  
Andrea Bonito ◽  
Ronald DeVore ◽  
Diane Guignard ◽  
Peter Jantsch ◽  
Guergana Petrova
Keyword(s):  
Polynomial Approximation ◽  
Analytic Functions ◽  
Several Variables

scholarly journals Best polynomial approximation in Besov spaces

1997 ◽  
Vol 85 (2) ◽  
pp. 315-323
Author(s):  
Francisco Pérez Acosta
Keyword(s):  
Polynomial Approximation ◽  
Besov Spaces ◽  
Best Polynomial Approximation

The Degree Of Polynomial Approximation And Interpolation Of Analytic Functions

1988 ◽  
Vol 13 (1-2) ◽  
pp. 81-98 ◽  
Author(s):  
M. Freund
Keyword(s):  
Polynomial Approximation ◽  
Analytic Functions

Best polynomial approximation in Sobolev-Laguerre and Sobolev-Legendre spaces

2002 ◽  
Vol 18 (4) ◽  
pp. 551-568 ◽  
Author(s):  
D. H. Kim ◽  
S. H. Kim ◽  
K. H. Kwon ◽  
Xin Li
Keyword(s):  
Polynomial Approximation ◽  
Best Polynomial Approximation
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