Divergence of wavelet series: A multifractal analysis

[en] We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper bounds for the Hausdorff dimensions of the sets of points where a given rate of divergence occurs, and we show that these bounds are generically optimal, according to several notions of genericity.

Disciplines :

Mathematics

Author, co-author :

Esser, Céline ; Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Jaffard, Stéphane ; Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Language :

English

Title :

Divergence of wavelet series: A multifractal analysis

Publication date :

2018

Journal title :

Advances in Mathematics

ISSN :

0001-8708

eISSN :

1090-2082

Publisher :

Elsevier, Atlanta, United States

Volume :

328

Pages :

928-958

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 17 January 2017

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