modulus of continuity

Absolute Convergence of Single and Double Fourier Series on Multiplicative Systems

Authors: Volosivets S. S.

Two-dimensional analogs of famous Zygmund and Szasz tests for absolute convergence of Fourier – Vilenkin series are established. Also it is proved that two-dimensional Szasz test is the best possible in the certain sense.

Approximation of Functions of Bounded p-variation by Euler Means

Authors: Tyuleneva A. A.

In this paper we study the Euler means
eqn(f)(x) =∑k=0n(nk)qn−k(1 + q)−nSk(f)(x), q > 0, n ∈ Z+,

Approximation of Functions by Fourier–Haar Sums in Weighted Variable Lebesgue and Sobolev Spaces

Authors: Magomed-Kasumov M. G.

It is considered weighted variable Lebesgue Lp(x)w and Sobolev Wp(⋅),w spaces with conditions on exponent p(x)≥1 and weight w(x) that provide Haar system to be a basis in Lp(x)w. In such spaces there were obtained estimates of Fourier–Haar sums convergence speed. Estimates are given in terms of modulus of continuity Ω(f,δ)p(⋅),w, based on mean shift (Steklov's function).

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.