Reference : Some prevalent results about strongly monoHölder functions
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/67505
Some prevalent results about strongly monoHölder functions
English
Clausel, Marianne [Université Paris Est > UMR 8050 du CNRS > Laboratoire d'analyse et de mathématiques appliquées > >]
Nicolay, Samuel mailto [Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes >]
2010
Nonlinearity
Institute of Physics
23
2101-2116
Yes (verified by ORBi)
International
0951-7715
[en] prevalence ; Hölder regularity ; dimension of the graph ; wavelets
[en] We study the typical behaviour of strongly monoHölder functions from the prevalence point of view. To this end we first prove wavelet-based criteria for strongly monoHölder functions. We then use the notion of prevalence to show that the functions of $C^\alpha (R^d)$ are almost surely strongly monoHölder with Hölder exponent $\alpha$. Finally, we prove that for any $\alpha\in (0, 1)$ on a prevalent set of $C^\alpha (R^d)$ the Hausdorff dimension of the graph is equal to $d +1-\alpha$.
http://hdl.handle.net/2268/67505
10.1088/0951-7715/23/9/004

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