The spectrum of singularities of Riemann's function
type: Item
instance of: scholarly article
title: The spectrum of singularities of Riemann's function
zbMATH Open document ID: 0889.26005
DOI: 10.4171/RMI/203
author: Stéphane Jaffard
published in: Revista Matemática Iberoamericana
publication date: 1998-05-29T00:00:00Z
full work available at URL: https://eudml.org/doc/39503
review text: For the Riemann's function \(\varphi (x)=\sum_{n=1}^\infty \frac 1{n^2}\sin \pi n^2x,\) the spectrum of singularities \(d(\alpha )\) is determined, where \(d(\alpha )\) denotes the Hausdorff dimension of the set of points and \(\varphi \) is Hölder-regular of order \(\alpha\). Furthermore, \(d\) satisfies the so called ``multifractal formalism for functions''.
Mathematics Subject Classification ID: 26A27
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 933290
zbMATH Keywords: Hölder regularity
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: wavelet
zbMATH Keywords: continued fractions
zbMATH Keywords: Riemann's function
reviewed by: Valeriu Anisiu
MaRDI profile type: Publication
OpenAlex ID: W2079081125
description: scientific article; zbMATH DE number 933290