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.

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 Construction of Schauder decomposition on banach spaces of periodic functions

1998 ◽  
Vol 41 (1) ◽  
pp. 61-91 ◽  
Author(s):  
Say Song Goh ◽  
S. L. Lee ◽  
Zuowei Shen ◽  
W. S. Tang
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Banach Spaces ◽  
Biorthogonal System ◽  
The Other ◽  
Projection Operators ◽  
Reconstruction Algorithms ◽  
Periodic Functions ◽  
Orthogonal Projections ◽  
Wavelet Decompositions

This paper deals with Schauder decompositions of Banach spaces X2π of 2π-periodic functions by projection operators Pk onto the subspaces Vk, k = 0,1,…, which form a multiresolution of X2π,. The results unify the study of wavelet decompositions by orthogonal projections in the Hilbert space on one hand and by interpolatory projections in the Banach space C2π on the other. The approach, using “orthogonal splines”, is constructive and leads to the construction of a Schauder decomposition of X2π and a biorthogonal system for X2π, and its dual X2π. Decomposition and reconstruction algorithms are derived from the construction.

scholarly journals Estimates of approximative characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of several variables with given majorant of mixed moduli of continuity in the space $L_{q}$

2019 ◽  
Vol 11 (2) ◽  
pp. 281-295 ◽  
Author(s):  
O.V. Fedunyk-Yaremchuk ◽  
S.B. Hembars'ka
Keyword(s):  
Linear Operators ◽  
Exact Order ◽  
Moduli Of Continuity ◽  
Periodic Functions ◽  
Several Variables

In this paper, we continue the study of approximative characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of several variables whose majorant of the mixed moduli of continuity contains both exponential and logarithmic multipliers. We obtain the exact-order estimates of the orthoprojective widths of the classes $B^{\Omega}_{p,\theta}$ in the space $L_{q},$ $1\leq p<q<\infty,$ and also establish the exact-order estimates of approximation for these classes of functions in the space $L_{q}$ by using linear operators satisfying certain conditions.

scholarly journals Approximation of classes of periodic functions of several variables with given majorant of mixed moduli of continuity

2021 ◽  
Vol 13 (3) ◽  
pp. 838-850
Author(s):  
O.V. Fedunyk-Yaremchuk ◽  
S.B. Hembars'ka
Keyword(s):  
Linear Operators ◽  
Exact Order ◽  
Moduli Of Continuity ◽  
Periodic Functions ◽  
Several Variables

In this paper, we continue the study of approximation characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of several variables whose majorant of the mixed moduli of continuity contains both exponential and logarithmic multipliers. We obtain the exact-order estimates of the orthoprojective widths of the classes $B^{\Omega}_{p,\theta}$ in the space $L_{q},$ $1\leq p<q<\infty,$ and also establish the exact-order estimates of approximation for these classes of functions in the space $L_{q}$ by using linear operators satisfying certain conditions.

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