Wavelets Techniques for Pointwise Anti-Hölderian Irregularity

Clausel, Marianne; Nicolay, Samuel

doi:10.1007/s00365-010-9120-9

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Wavelets Techniques for Pointwise Anti-Hölderian Irregularity

Clausel, Marianne; Nicolay, Samuel

2011 • In Constructive Approximation, 33, p. 41-75

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https://hdl.handle.net/2268/79758

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10.1007/s00365-010-9120-9

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Keywords :

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

Publication date :

2011

Journal title :

Constructive Approximation

ISSN :

0176-4276

eISSN :

1432-0940

Publisher :

Springer

Volume :

Pages :

41-75

Peer reviewed :

Peer Reviewed verified by ORBi

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since 18 December 2010

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