ряд Фурье

Approximation of Continuous 2 p-Periodic Piecewise Smooth Functions by Discrete Fourier Sums

Authors: Akniev G. G.

Let N be a natural number greater than 1. Select N uniformly distributed points tk = 2πk/N + u (0 6 k 6 N − 1), and denote by Ln,N(f) = Ln,N(f,x) (1 6 n 6 N/2) the trigonometric polynomial of order n possessing the least quadratic deviation from f with respect to the system {tk}N−1 k=0 . Select m + 1 points −π = a0 < a1 < ... < am−1 < am = π, where m > 2, and denote Ω = {ai}m i=0. Denote by Cr Ω a class of 2π-periodic continuous functions f, where f is r-times differentiable on each segment ∆i = [ai,ai+1] and f(r) is absolutely continuous on ∆i.

Λ-Summability and Multiplicators of Holder Classes of Fourierseries with Respect ̈ to Character Systems

Authors: Agafonova N. Y.

Let G be a Vilenkin group of bounded type. We obtain nessesary and sufficient conditions of uniform Λ-summability for all Fourier series of f ∈ C(G) and one of Λ-summability in L 1 (G) for all Fourier series of f ∈ L 1 (G). Also we extend some T. Quek and L. Yap results to the case of general modulus of continuity.

On Uniform Convergenceof Transformationsof Fourier Serieson Multiplicative Systems

Authors: Agafonova N. Y.

Necessary and suffiecient conditions for uniform Λ-summability of Fourier – Vilenkin series of Functions from Orlicz spaces LΦ[0,1) and L1[0,1) are obtained. Some corollaries for matrices with generalized monotone coeffiecients are given.

Harmonic Analysis of Periodic at Infinity Functions from Stepanov Spaces

Authors: Strukova I. I.

We consider Stepanov spaces of functions defined on R with their values in a complex Banach space. We introduce the notions of slowly varying and periodic at infinity functions from Stepanov space. The main results of the article are concerned with harmonic analysis of periodic at infinity functions from Stepanov space. For this class of functions we introduce the notion of a generalized Fourier series; the Fourier coefficients in this case may not be constants, they are functions that are slowly varying at infinity.

About harmonic analysis of periodic at infinity functions

Authors: Strukova I. I.

We consider slowly varying and periodic at infinity multivariable functions in Banach space. We introduce the notion of Fourier series of periodic at infinity function, study the properties of Fourier series and their convergence. Basic results are derived with the use of isometric representations theory.