Interpolation of sequences
type: Item
instance of: scholarly article
title: Interpolation of sequences
zbMATH Open document ID: 1117.54043
author: Raúl Naulin M.
author: Carlos Uzcátegui
published in: Real Analysis Exchange
publication date: 2006-11-13T00:00:00Z
review text: Benyamini has shown that there is a continuous function \(f\colon \mathbb{R}\to \mathbb{R}\) such that for any sequence \((x_n)_{n\in\mathbb{Z}}\in [0,1]^{\mathbb{Z}}\), there is \(t\in \mathbb{R}\) such that \(x_n = f(t+n)\) for all \(n\in \mathbb{Z}\). Such a function is said to interpolate all sequences in \([0,1]^{\mathbb{Z}}\). In this note the authors extend Benyamini's result. More specifically, they show that there is a continuous function \(f\colon \mathbb{R}\setminus\mathbb{Q}\to \mathbb{R}\) that interpolates all sequences in \(\mathbb{R}^{\mathbb{Z}}\). This can also be done by a Baire class-1 function \(f\colon \mathbb{R}\to \mathbb{R}\).
reviewed by: Jan van Mill
Mathematics Subject Classification ID: 54E45
Mathematics Subject Classification ID: 54H05
zbMATH DE Number: 5071510
zbMATH Keywords: interpolation
zbMATH Keywords: sequences
zbMATH Keywords: Cantor set
MaRDI profile type: Publication
full work available at URL: realanalexch.31.2.0519
OpenAlex ID: W1603146974
DOI: 10.14321/REALANALEXCH.31.2.0519
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description: scientific article; zbMATH DE number 5071510