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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 ${ψ_{k}}_{k \in ℤ}$ such that ${ψ_{k}; k \in ℤ} = X$ and $ψ_{k} = ψ_{k + l q (k)}$ , $l \in ℤ$ for all $k$ and some $q (k) \in ℕ$ which depends on $k$ .

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

Alexandr Fischer (2012)

Mathematica Bohemica

The paper is the extension of the author's previous papers and solves more complicated problems. Almost periodic solutions of a certain type of almost periodic linear or quasilinear systems of neutral differential equations are dealt with.

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.

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

Alexandr Fischer (2004)

Mathematica Bohemica

This paper is a continuation of my previous paper in Mathematica Bohemica and solves the same problem but by means of another method. It deals with almost periodic solutions of a certain type of almost periodic systems of differential equations.

Almost periodic Sturm-Liouville operators with Cantor homogeneous spectrum.

Mikhail Sodin, Peter Yuditskii (1995)

Commentarii mathematici Helvetici

Almost periodicity of some error terms in prime number theory

Jerzy Kaczorowski, Olivier Ramaré (2003)

Acta Arithmetica

Almost-periodic solutions in various metrics of higher-order differential equations with a nonlinear restoring term

Ján Andres, Alberto Maria Bersani, Lenka Radová (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Almost-periodic solutions in various metrics (Stepanov, Weyl, Besicovitch) of higher-order differential equations with a nonlinear Lipschitz-continuous restoring term are investigated. The main emphasis is focused on a Lipschitz constant which is the same as for uniformly almost-periodic solutions treated in [A1] and much better than those from our investigations for differential systems in [A2], [A3], [AB], [ABL], [AK]. The upper estimates of $ε$ for $ε$ -almost-periods of solutions and their derivatives...

An analogue of the argument theorem of Bohr and its application

Wojciech Chojnacki (1984)

Studia Mathematica

Analyse 2-microlocale et développementen série de chirps d'une fonction de Riemann et de ses généralisations

Daniel Boichu (1994)

Colloquium Mathematicae

En dimension 1 on analyse la fonction irrégulière $r (x) = \sum_{n = 1}^{\infty} n^{- p} s i n (n^{p} x)$ (p entier ≥ 2) en un point $x_{0}$ de dérivabilité (π est un tel point) et on démontre que le terme d’erreur est un chirp de classe (1 + 1/(2p-2), 1/(p-1), (p-1)/p). La fonction r(x) est dans l’espace 2-microlocal $C_{x_{0}}^{s, s^{'}}$ si et seulement si s+s’ ≤ 1 - 1/p et ps+s’≤ p - 1/2. En dimension 2, on obtient en (π,π) l’existence d’un plan tangent pour la surface $z = \sum_{m, n = 1}^{\infty} {(m^{2} + n^{2})}^{- γ} s i n (m^{2} x + n^{2} y)$ dès que γ>1.

Analysis of two step nilsequences

Bernard Host, Bryna Kra (2008)

Annales de l’institut Fourier

Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg’s proof of Szemerédi’s Theorem and have since played a role in problems in additive combinatorics. Nilsequences are a generalization of almost periodic sequences and we study which portions of the classical theory for almost periodic sequences can be generalized for two step nilsequences. We state and prove basic properties for two step nilsequences and give a classification scheme for them.

Approximation of almost periodic functions by convolution type operators.

A. Pych-Taberska, M. Topolewska (1996)

Revista Matemática de la Universidad Complutense de Madrid

Approximation of almost periodic functions by periodic ones

Alexander Fischer (1998)

Czechoslovak Mathematical Journal

It is not the purpose of this paper to construct approximations but to establish a class of almost periodic functions which can be approximated, with an arbitrarily prescribed accuracy, by continuous periodic functions uniformly on $ℝ = (- \infty; + \infty)$ .

Approximation properties of the partial sums of Fourier series of some almost periodic functions

Paulina Pych-Taberska (1990)

Studia Mathematica

Block Toeplitz operators with frequency-modulated semi-almost periodic symbols.

Böttcher, A., Grudsky, S., Spitkovsky, I. (2003)

International Journal of Mathematics and Mathematical Sciences

Caratterizzazione dei polinomi di convoluzione in una variabile a decrescenza rapida, a coefficienti costanti, che hanno soluzioni quasi periodiche per ogni termine noto quasi periodico

Giuliano Bratti (1972)

Rendiconti del Seminario Matematico della Università di Padova

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