An adapted group-dilation anisotropic multifractal formalism for functions

DOI

10.2991/jnmp.2008.15.1.9How to use a DOI?

Abstract

Anisotropic phenomena can be observed almost everywhere in nature. This makes them important sub jects for theoretical and experimental studies. In this work, we focus on the study of anisotropic quasi-self-similar signals. It holds that the classical multifractal formalism in all its formulations does not hold for this class. We then use an homogeneous norm introduced by Calderon and Torchinsky to check the validity of an adapted anisotropic multifractal formalism for these signals. Our techniques are based on group theory combined with wavelet characterization of anisotropic function spaces. We then show the efficiency of anisotropic wavelets in detecting singularities.

Copyright

© 2008, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Anouar Ben Mabrouk
PY  - 2008
DA  - 2008/03/01
TI  - An adapted group-dilation anisotropic multifractal formalism for functions
JO  - Journal of Nonlinear Mathematical Physics
SP  - 117
EP  - 139
VL  - 15
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.1.9
DO  - 10.2991/jnmp.2008.15.1.9
ID  - Mabrouk2008
ER  -