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Pointwise analysis of Riemann's “nondifferentiable” function

Holschneider, Matthias; Tchamitchian, Philippe (1991), Pointwise analysis of Riemann's “nondifferentiable” function, Inventiones Mathematicae, 105, 1, p. 157-175. http://dx.doi.org/10.1007/BF01232261

Type
Article accepté pour publication ou publié
Date
1991
Journal name
Inventiones Mathematicae
Volume
105
Number
1
Publisher
Springer
Pages
157-175
Publication identifier
Metadata
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Author(s)
Holschneider, Matthias
Tchamitchian, Philippe
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.
Subjects / Keywords
function of Riemann