Multifractal Formalism for Selfsimilar Functions Expanded in Singular Basis

✍ Scribed by Mourad Ben Slimane

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 266 KB
• Volume: 11
• Category: Article
• ISSN: 1063-5203
• DOI: 10.1006/acha.2001.0364

✦ Synopsis

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.