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Absolutely convergent Fourier series and generalized Lipschitz classes of functions

Ferenc Móricz (2008)

Colloquium Mathematicae

We investigate the order of magnitude of the modulus of continuity of a function f with absolutely convergent Fourier series. We give sufficient conditions in terms of the Fourier coefficients in order that f belong to one of the generalized Lipschitz classes Lip(α,L) and Lip(α,1/L), where 0 ≤ α ≤ 1 and L = L(x) is a positive, nondecreasing, slowly varying function such that L(x) → ∞ as x → ∞. For example, a 2π-periodic function f is said to belong to the class Lip(α,L) if | f ( x + h ) - f ( x ) | C h α L ( 1 / h ) for all x ∈ , h >...

Accelerating the convergence of trigonometric series

Anry Nersessian, Arnak Poghosyan (2006)

Open Mathematics

A nonlinear method of accelerating both the convergence of Fourier series and trigonometric interpolation is investigated. Asymptotic estimates of errors are derived for smooth functions. Numerical results are represented and discussed.

Algebrability of the set of non-convergent Fourier series

Richard M. Aron, David Pérez-García, Juan B. Seoane-Sepúlveda (2006)

Studia Mathematica

We show that, given a set E ⊂ 𝕋 of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t ∈ E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra of 𝓒(𝕋) every non-zero element of which has a Fourier series expansion divergent in E.

Almost everywhere convergence of convolution powers on compact abelian groups

Jean-Pierre Conze, Michael Lin (2013)

Annales de l'I.H.P. Probabilités et statistiques

It is well-known that a probability measure μ on the circle 𝕋 satisfies μ n * f - f d m p 0 for every f L p , every (some) p [ 1 , ) , if and only if | μ ^ ( n ) | l t ; 1 for every non-zero n ( μ is strictly aperiodic). In this paper we study the a.e. convergence of μ n * f for every f L p whenever p g t ; 1 . We prove a necessary and sufficient condition, in terms of the Fourier–Stieltjes coefficients of μ , for the strong sweeping out property (existence of a Borel set B with lim sup μ n * 1 B = 1 a.e. and lim inf μ n * 1 B = 0 a.e.). The results are extended to general compact Abelian groups G with Haar...

Almost periodic sequences and functions with given values

Michal Veselý (2011)

Archivum Mathematicum

We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set  X in a metric space, it is proved the existence of an almost periodic sequence { ψ k } k such that { ψ k ; k } = X and ψ k = ψ k + l q ( k ) , l for all  k and some q ( k ) which depends on  k .

Almost periodic solutions with a prescribed spectrum of systems of linear and quasilinear differential equations with almost periodic coefficients and constant time lag (Cauchy integral)

Alexandr Fischer (1999)

Mathematica Bohemica

This paper generalizes earlier author's results where the linear and quasilinear equations with constant coefficients were treated. Here the method of limit passages and a fixed-point theorem is used for the linear and quasilinear equations with almost periodic coefficients.

Currently displaying 101 – 120 of 1343