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Singularity spectrum of multifractal functions involving oscillating singularities |
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| Authors: | A Arneodo E Bacry S Jaffard J F Muzy |
| Institution: | (1) Centre de Recherche Paul Pascal, Avenue Schweitzer, 33600 Pessac, France;(2) Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau, France;(3) Départment de Mathématiques Université Paris XII, 61 Avenue du Général de Gaulle, 94010 Créteil, France;(4) CMLA, ENS Cachan, 61 Avenue du Président Wilson, 94235 Cachan, France |
| Abstract: | We give general mathematical results concerning oscillating singularities and we study examples of functions composed only of oscillating singularities. These functions are defined by explicit coefficients on an orthonormal wavelet basis. We compute their Hölder regularity and oscillation at every point and we deduce their spectrum of oscillating singularities. |
| Keywords: | 26A15 33A65 |
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