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Multifractal formalism for selfsimilar functions associated to the $n$-scale dilation family

Published online by Cambridge University Press:  15 January 2004

MOURAD BEN SLIMANE
MOURAD BEN SLIMANE
Affiliation:
Département de Mathématiques, Faculté des Sciences de Tunis, 1060 Tunis, Tunisia. e-mail: Mourad.BenSlimane@fst.rnu.tn
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Abstract

The multifractal formalism for functions has been proved to be valid for a large class of selfsimilar functions. All the functions that have been studied are (or turned out to be) associated with a family of contractions which satisfies some separation conditions. In this paper, we extend the validity in the presence of overlaps involved by the well-known $n$-scale dilation family. Our method of proof is based on wavelet analysis and some interesting properties of this family.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 136 , Issue 1 , January 2004 , pp. 195 - 212
Copyright
2004 Cambridge Philosophical Society

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