\(C^{(\infty)}_a\)-almost periodic functions
type: Item
instance of: scholarly article
title: \(C^{(\infty)}_a\)-almost periodic functions
zbMATH Open document ID: 0963.42008
author: Marek Adamczak
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 2001-06-28T00:00:00Z
review text: There is considered the space \(C^{(\infty)}_a(\mathbb{R})\) with convergence defined by means of the functional \[ D^{(\infty)}_a(f)= \sup_{t\in\mathbb{R}} \sum^\infty_{i=0} a_i|f^{(i)}(t)| \] with \(a_0= 1\), \(a_i> 0\) for all \(i\). The notion of \(C^{(\infty)}_a\)-almost periodicity in \(C^{(\infty)}(\mathbb{R})\) by means of the functional \(D^{(\infty)}_a\) is defined and the properties of \(C^{(\infty)}_a\)-a.p. functions are investigated. There is proved a theorem on approximation of \(C^{(\infty)}_a\)-continuous functions by means of their Steklov functions (i.e., integral means).
Mathematics Subject Classification ID: 42A75
zbMATH DE Number: 1442080
zbMATH Keywords: uniformly almost periodic function
zbMATH Keywords: infinitely differentiable function
zbMATH Keywords: Steklov function
reviewed by: Julian Musielak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1442080