On the jackson theorem for periodic functions in spaces with integral metric

2000 ◽  
Vol 52 (1) ◽  
pp. 133-147 ◽  
Author(s):  
S. A. Pichugov
Keyword(s):  
Periodic Functions ◽  
Jackson Theorem

On the Jackson theorem for periodic functions in metric spaces with integral metric. II

2012 ◽  
Vol 63 (11) ◽  
pp. 1733-1744 ◽  
Author(s):  
S. A. Pichugov
Keyword(s):  
Metric Spaces ◽  
Periodic Functions ◽  
Jackson Theorem

scholarly journals Approximation by algebraic polynomials in metric spaces $L_{\psi}$

2013 ◽  
Vol 21 ◽  
pp. 3
Author(s):  
T.A. Agoshkova
Keyword(s):  
Modulus Of Continuity ◽  
Metric Spaces ◽  
Jackson Inequality ◽  
Algebraic Polynomials ◽  
Periodic Functions ◽  
Jackson Theorem ◽  
Approximation By Algebraic Polynomials

In the space $L_{\psi}[-1;1]$ of non-periodic functions with metric $\rho(f,0)_{\psi} = \int\limits_{-1}^1 \psi(|f(x)|)dx$, where $\psi$ is a function of the type of modulus of continuity, we study Jackson inequality for modulus of continuity of $k$-th order in the case of approximation by algebraic polynomials. It is proved that the direct Jackson theorem is true if and only if the lower dilation index of the function $\psi$ is not equal to zero.

The Numerical Scheme without Saturation for Periodic Functions

2018 ◽  
Vol 481 (4) ◽  
pp. 362-366
Author(s):  
A. Petrov ◽  
Keyword(s):  
Numerical Scheme ◽  
Periodic Functions

(VC)(n)-ALMOST PERIODIC FUNCTIONS

1999 ◽  
Vol 32 (2) ◽  
Author(s):  
Stanislaw Stoinski
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions

On finite sums of periodic functions

2020 ◽  
Vol 27 (2) ◽  
pp. 265-269
Author(s):  
Alexander Kharazishvili
Keyword(s):  
Analytic Function ◽  
Real Line ◽  
Real Analytic Function ◽  
Periodic Functions ◽  
Uniform Limit ◽  
The Real ◽  
Pointwise Limit ◽  
Finite Sums ◽  
Real Analytic

AbstractIt is shown that any function acting from the real line {\mathbb{R}} into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function {x\rightarrow\exp(x^{2})} cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, this function is a locally uniform limit of finite sums of periodic functions. The latter fact needs the techniques of Hamel bases.

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