A Weak Local Irregularity Property in Sν Spaces

Clausel, Marianne; Nicolay, Samuel

doi:10.1007/s00009-017-0902-1

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A Weak Local Irregularity Property in Sν Spaces

Clausel, Marianne; Nicolay, Samuel

2017 • In Mediterranean Journal of Mathematics, 14 (3), p. 102

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https://hdl.handle.net/2268/211725

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10.1007/s00009-017-0902-1

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Keywords :

prevalence; generic properties of functions; sequence spaces

Abstract :

[en] It has been shown that, from the prevalence point of view, elements of the Sν spaces are almost surely multifractal, while the Hölder exponent at almost every point is almost surely equal to the maximum Hölder exponent. We show here that typical elements of Sν are very irregular by proving that they almost surely satisfy a weak irregularity property: there exists a local irregularity exponent which is constant for almost every element of Sν and equal to the lowest Hölder exponent.

Disciplines :

Mathematics

Author, co-author :

Clausel, Marianne

Nicolay, Samuel ; Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Language :

English

Title :

A Weak Local Irregularity Property in Sν Spaces

Publication date :

2017

Journal title :

Mediterranean Journal of Mathematics

ISSN :

1660-5446

eISSN :

1660-5454

Publisher :

Springer

Volume :

Issue :

Pages :

102

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.springer.com/article/10.1007/s00009-017-0902-1?no-access=true

Available on ORBi :

since 12 June 2017

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