Pointwise analysis of Riemann's ``nondifferentiable'' function
type: Item
instance of: scholarly article
title: Pointwise analysis of Riemann's ``nondifferentiable'' function
zbMATH Open document ID: 0741.26004
DOI: 10.1007/BF01232261
published in: Inventiones Mathematicae
publication date: 1992-06-26T00:00:00Z
full work available at URL: https://eudml.org/doc/143908
review text: We show how to analyse the local regularity of functions with the help of the wavelet transform. These results will be applied to the function of Riemann, where we show the existence of a dense set of points where this function is differentiable. On another dense set we show the existence of local singularities of cusp type. On a third set we show differentiability to the right (left). On the remaining set the function will be shown to be not differentiable.
Mathematics Subject Classification ID: 26A27
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 22012
zbMATH Keywords: Riemann's nondifferentiable function
zbMATH Keywords: local regularity of functions
zbMATH Keywords: wavelet transform
author: Matthias Holschneider
author: Philippe Tchamitchian
MaRDI profile type: Publication
cites work: The Differentiability of the Riemann Function at Certain Rational Multiples of &#960
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OpenAlex ID: W2044023594
description: scientific article; zbMATH DE number 22012