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Pointwise analysis of Riemann's “nondifferentiable” function

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Date
1991
Dewey
Analyse
Sujet
function of Riemann
Journal issue
Inventiones Mathematicae
Volume
105
Number
1
Publication date
1991
Article pages
157-175
Publisher
Springer
DOI
http://dx.doi.org/10.1007/BF01232261
URI
https://basepub.dauphine.fr/handle/123456789/14075
Collections
  • CEREMADE : Publications
Metadata
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Author
Holschneider, Matthias
Tchamitchian, Philippe
Type
Article accepté pour publication ou publié
Abstract (EN)
We will 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 functions will be shown to be not differentiable.

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