Resolution of an integral equation with the Thue-Morse sequence
type: Item
instance of: scholarly article
title: Resolution of an integral equation with the Thue-Morse sequence
zbMATH Open document ID: 1259.45002
author: Jean-François Bertazzon
published in: Indagationes Mathematicae. New Series
publication date: 2012-08-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1201.2502
reviewed by: Stefan Balint
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 6070485
zbMATH Keywords: integral equation
zbMATH Keywords: Thue-Morse sequence
MaRDI profile type: Publication
OpenAlex ID: W3101232226
arXiv ID: 1201.2502
cites work: Répartition des suites (nα)n∈Net substitutions
cites work: A relative of the Thue-Morse sequence
cites work: Uniform distribution mod 1
cites work: Some combinatorial properties of the Thue-Morse sequence and a problem in semigroups
cites work: On the one-sided boundedness of sums of fractional parts \((\{ n\alpha+ \gamma\}-\frac12)\).
cites work: The Thue-Morse-Pascal double sequence and similar structures
DOI: 10.1016/J.INDAG.2012.01.003
review text: The author shows that there exists a continuous function \(f(x)\) valued in \([-1,1]\) solving the equation NEWLINE\[NEWLINE\int^x_0 f(t)\,dt+ f(0)= f\Biggl({x\over 2}\Biggr)NEWLINE\]NEWLINE and having the following properties:NEWLINENEWLINE(1) for each integer \(n\), \(f(2n+1)= u_n\) and \(f(2n)= 0\),NEWLINENEWLINE (2) for each negative real number \(x\), \(f(x)= 0\),NEWLINENEWLINE (3) for each positive real number \(x\), \(|f(x)|= |f(x+2)|\), where \(u_n\) is the Thue-Morse sequence.
description: scientific article; zbMATH DE number 6070485