Multifractal Formalism for Selfsimilar Functions Expanded in Singular Basis
Journal Article
رابط المنشور على الويب:
المجلة \ الصحيفة:
Applied and Computational Harmonic Analysis
رقم العدد:
Volume 11, Issue 3, November 2001,
رقم الإصدار السنوي:
Volume 11, Issue 3, November 2001,
الصفحات:
387-419
مستخلص المنشور:
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.