Pointwise analysis of Riemann’s “nondifferentiable” function. (English) Zbl 0741.26004

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.
Reviewer: M.Holschneider


26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
42C15 General harmonic expansions, frames
Full Text: DOI EuDML


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