Exact and asymptotic estimates forn-widths of some classes of periodic functions

1992 ◽  
Vol 8 (3) ◽  
pp. 289-307 ◽  
Author(s):  
Han-lin Chen ◽  
Chun Li
Keyword(s):  
Asymptotic Estimates ◽  
Periodic Functions

scholarly journals On approximation, in the strong sense, of functions of two variables by trigonometric polynomials

2021 ◽  
pp. 20
Author(s):  
V.V. Lipovik ◽  
N.P. Khoroshko
Keyword(s):  
Strong Sense ◽  
Trigonometric Polynomials ◽  
Asymptotic Estimates ◽  
Periodic Functions ◽  
Functions Of Two Variables

In the paper, we have found order asymptotic estimates of approximations, in the strong sense, relative to given matrix of classes of continuous periodic functions of two variables by some trigonometric polynomials.

scholarly journals Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness

2020 ◽  
Vol 17 (3) ◽  
pp. 396-413
Author(s):  
Anatolii Serdyuk ◽  
Igor Sokolenko
Keyword(s):  
Unit Ball ◽  
Fourier Coefficients ◽  
Asymptotic Estimates ◽  
Periodic Functions ◽  
High Smoothness ◽  
Uniform Approximations

We find two-sided estimates for the best uniform approximations of classes of convolutions of $2\pi$-periodic functions from a unit ball of the space $L_p, 1 \le p <\infty,$ with fixed kernels such that the moduli of their Fourier coefficients satisfy the condition $\sum\limits_{k=n+1}^\infty\psi(k)<\psi(n).$ In the case of $\sum\limits_{k=n+1}^\infty\psi(k)=o(1)\psi(n),$ the obtained estimates become the asymptotic equalities.

scholarly journals On a family of weighted convolution algebras

1990 ◽  
Vol 13 (3) ◽  
pp. 517-525 ◽  
Author(s):  
Hans G. Feichtinger ◽  
A. Turan Gürkanli
Keyword(s):  
Fourier Transforms ◽  
Locally Compact Abelian Group ◽  
Asymptotic Estimates ◽  
Locally Compact ◽  
Invariance Properties ◽  
Beurling Algebra ◽  
Convolution Algebras ◽  
Approximate Identities ◽  
Beurling Algebras ◽  
Banach Ideals

Continuing a line of research initiated by Larsen, Liu and Wang [12], Martin and Yap [13], Gürkanli [15], and influenced by Reiter's presentation of Beurling and Segal algebras in Reiter [2,10] this paper presents the study of a family of Banach ideals of Beurling algebrasLw1(G),Ga locally compact Abelian group. These spaces are defined by weightedLp-conditions of their Fourier transforms. In the first section invariance properties and asymptotic estimates for the translation and modulation operators are given. Using these it is possible to characterize inclusions in section 3 and to show that two spaces of this type coincide if and only if their parameters are equal. In section 4 the existence of approximate identities in these algebras is established, from which, among other consequences, the bijection between the closed ideals of these algebras and those of the corresponding Beurling algebra is derived.

(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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