Multifractal Formalism for Selfsimilar Functions Expanded in Singular Basis |
| |
Authors: | Mourad Ben Slimane |
| |
Institution: | Département de Mathématiques, Faculté des Sciences de Tunis, Campus universitaire, 1060, Tunis, Tunisiaf1 |
| |
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. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|