Sharp inequalities connected with estimates for approximations of periodic functions by means of moduli of continuity of their derivatives of odd order with different steps

2000 ◽  
Vol 101 (2) ◽  
pp. 2914-2929
Author(s):  
O. L. Vinogradov ◽  
V. V. Zhuk
Keyword(s):  
Moduli Of Continuity ◽  
Periodic Functions ◽  
Odd Order ◽  
Derivatives Of

scholarly journals On widths of some classes of functions with values in Hilbert space

2021 ◽  
Vol 17 ◽  
pp. 105
Author(s):  
S.V. Savela
Keyword(s):  
Hilbert Space ◽  
Moduli Of Continuity ◽  
Periodic Functions

We find the exact weak widths for one class of $2\pi$-periodic functions with values in Hilbert space, which is determined by moduli of continuity.

scholarly journals Inequalities for norms of derivatives of non-periodic functions with non-symmetric constraints on higher derivatives

2012 ◽  
Vol 20 ◽  
pp. 99
Author(s):  
V.A. Kofanov
Keyword(s):  
Real Line ◽  
Periodic Functions ◽  
Higher Derivatives ◽  
Derivatives Of

For non-periodic functions $x \in L^r_{\infty}(\mathbb{R})$ defined on the whole real line we established the analogs of certain inequality of V.F. Babenko.

scholarly journals Properties of extrema of estimates for middle derivatives of odd order in Sobolev classes

2019 ◽  
Vol 487 (5) ◽  
pp. 487-492
Author(s):  
T. A. Garmanova ◽  
I. A. Sheipak
Keyword(s):  
Sobolev Spaces ◽  
Global Maximum ◽  
Sobolev Classes ◽  
Odd Order ◽  
Derivatives Of

The embedding constants for the Sobolev spaces W2n[0;1]→W∞k[0; 1], 0 ≤ k ≤ n - 1 are considered. The properties of the functions An,k(x) arising in the inequalities |f(k)(x)|≤An,k (x)││f||W2n[0;1], are studied. The extremum points of An;k are calculated for k = 3, 5 and all admissible n. The global maximum of these functions is found, and the exact embedding constants are calculated.

Approximation of periodic functions in certain sub-classes of Lp[0,2π]

2017 ◽  
Vol 10 (03) ◽  
pp. 1750046
Author(s):  
Uaday Singh ◽  
Soshal Saini
Keyword(s):  
Fourier Series ◽  
Trigonometric Approximation ◽  
Moduli Of Continuity ◽  
Periodic Functions ◽  
Matrix Means ◽  
Approximation Of Periodic Functions

In this paper, we determine the degree of trigonometric approximation of [Formula: see text]-periodic functions and their conjugates, in terms of the moduli of continuity associated with them, by matrix means of corresponding Fourier series. We also discuss some analogous results with remarks and corollaries.

scholarly journals On optimal interval quadrature formulae on classes of differentiable periodic functions

2021 ◽  
Vol 15 ◽  
pp. 16
Author(s):  
V.F. Babenko ◽  
D.S. Skorokhodov
Keyword(s):  
Quadrature Formula ◽  
Invariant Set ◽  
Periodic Functions ◽  
Quadrature Formulae ◽  
Optimal Interval ◽  
Arbitrary Permutation ◽  
Derivatives Of

We solved the problem about the best interval quadrature formula on the class $W^r F$ of differentiable periodic functions with arbitrary permutation-invariant set $F$ of derivatives of order $r$. We proved that the formula with equal coefficients and $n$ node intervals, which have equidistant middle points, is the best on given class.

scholarly journals The best polynomial approximation, derivatives of fractional order, and widths of classes of functions in $L_2$

2016 ◽  
Vol 24 ◽  
pp. 10
Author(s):  
S.B. Vakarchuk ◽  
M.B. Vakarchuk
Keyword(s):  
Fractional Order ◽  
Polynomial Approximation ◽  
Fractional Derivatives ◽  
Periodic Functions ◽  
Best Polynomial Approximation ◽  
Alpha Beta ◽  
Derivatives Of

On the classes of $2\pi$-periodic functions ${\mathcal{W}}^{\alpha} (K_{\beta}, \Phi)$, where $\alpha, \beta \in (0;\infty)$, defined by $K$-functionals $K_{\beta}$, fractional derivatives of order $\alpha$, and majorants $\Phi$, the exact values of different $n$-widths have been computed in the space $L_2$.

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