A wavelet characterization for the upper global Hölder index

Marianne Clausel (1) , Nicolay Samuel (2)

1 SAM - Statistique Apprentissage Machine
2 Département de Mathématiques [Liège]

The upper Hölder index has been introduced to describe smoothness properties of a continuous function. It can be seen as the irregular counterpart of the usual Hölder index and has been used to investigate the behavior at the origin of the modulus of smoothness in many classical cases. In this paper, we prove a characterization of the upper Hölder index in terms of wavelet coefficients. This result is a first step in the estimation of this exponent using wavelet methods.

Mots clés: Uniform Hölder regularity; Uniform Hölder irregularity; Discrete wavelet transform

Domaines: Analyse fonctionnelle [math.FA]

Marianne Clausel, Nicolay Samuel. A wavelet characterization for the upper global Hölder index. Journal of Fourier Analysis and Applications, 2012, 18 (4), pp.750-769. ⟨10.1007/s00041-012-9220-y⟩. ⟨hal-00582856⟩