Some remarks on Bohr's almost periodic functions and Stepanov's almost periodic functions
type: Item
instance of: scholarly article
title: Some remarks on Bohr's almost periodic functions and Stepanov's almost periodic functions
zbMATH Open document ID: 0884.42006
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 1998-04-02T00:00:00Z
review text: There are considered V-a.p. functions and L-a.p. functions \(x\) on the real line (i.e., almost periodic in the sense of variation and in the sense of Lipschitz condition, respectively). It is proved that if \(x\) is S-a.p. and the indefinite integral of \(x\) is bounded and uniformly continuous, then this integral is V-a.p. Moreover, if \(x\) is u.a.p., then its integral means \(S_x(u,h)= {1\over 2h} \int^{u+ h}_{u- h}x(s)ds\) are L-a.p. for every \(u\in\mathbb{R}\) and \(S_x(u, h)\to x(u)\) as \(h\to 0\) uniformly for \(u\in\mathbb{R}\).
Mathematics Subject Classification ID: 42A75
Mathematics Subject Classification ID: 26A45
zbMATH DE Number: 1078851
zbMATH Keywords: almost periodic functions
zbMATH Keywords: approximation
zbMATH Keywords: functions of finite variation
zbMATH Keywords: Lipschitz condition
author: Stanisław Stoiński
reviewed by: Julian Musielak
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1078851