Article (Scientific journals)
Divergence of wavelet series: A multifractal analysis
Esser, Céline; Jaffard, Stéphane
2018In Advances in Mathematics, 328, p. 928-958
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Keywords :
Baire genericity; Besov sequence spaces; Divergence properties; Hausdorff dimension; Lineability; Multifractal Analysis; Prevalence; Wavelet Series
Abstract :
[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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