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On lacunary wavelet series. (English) Zbl 1063.60053
Summary: We prove that the Hölder singularities of random lacunary wavelet series are chirps located on random fractal sets. We determine the Hausdorff dimensions of these singularities, and the a.e. modulus of continuity of the series. Lacunary wavelet series thus turn out to be a new example of multifractal functions.

MSC:
60G17 Sample path properties
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
28A80 Fractals
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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