Abstract
Selfsimilar functions can be written as the superposition of similar structures, at different scales, generated by a function
g. Their expressions look like wavelet decompositions. In the case where
g is regular, the multifractal formalism has been proved for the corresponding selfsimilar function, for Hölder exponents smaller than the regularity of
g. In this paper, we show, in the case where
g is the Schauder function (or the Haar function or a spline-type wavelet), that for larger Hölder exponents, the singularities of
g can disturb the Hölder exponents of the associated selfsimilar function, modify the shape of the spectrum of singularities, and finally affect the validity of the multifractal formalism.