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In this paper we introduce and study the self-similar functions. We prove that these functions have a concave spectrum (increasing and then decreasing) and that the different formulas that were proposed for the multifractal formalism allow us to determine either the whole increasing part of their spectrum or a part of it. One of these methods (the wavelet-maxima method) yields their complete spectrum.
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Stéphane Jaffard (1997) studied this question.
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