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

Journal Article

• رابط المنشور على الويب: https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/multifractal-for
• المجلة \ الصحيفة: Mathematical Proceedings of the Cambridge Philosophical Society
• رقم العدد: 136(2004)
• رقم الإصدار السنوي: 136(2004)
• الصفحات: 195-212

مستخلص المنشور

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.