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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.

Information

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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