Pointwise Hölder regularity; Wavelets; Spectrum of singularities; Multifractal formalism
Abstract :
[en] In this paper, we introduce a notion of weak pointwise Hölder regularity,
starting from the definition of the pointwise anti-Hölder irregularity. Using this concept,
a weak spectrum of singularities can be defined as for the usual pointwise Hölder
regularity.We build a class of wavelet series satisfying the multifractal formalism and
thus show the optimality of the upper bound. We also show that the weak spectrum
of singularities is disconnected from the casual one (referred to here as strong spectrum
of singularities) by exhibiting a multifractal function made of Davenport series
whose weak spectrum differs from the strong one.
Disciplines :
Mathematics
Author, co-author :
Clausel, Marianne
Nicolay, Samuel ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Language :
English
Title :
Wavelets Techniques for Pointwise Anti-Hölderian Irregularity
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