Journal of Nonlinear Mathematical Physics

Volume 15, Issue 1, March 2008, Pages 117 - 139

An adapted group-dilation anisotropic multifractal formalism for functions

Authors
Anouar Ben Mabrouk
Corresponding Author
Anouar Ben Mabrouk
Received 11 September 2007, Accepted 15 November 2007, Available Online 1 March 2008.
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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
15 - 1
Pages
117 - 139
Publication Date
2008/03/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2008.15.1.9How to use a DOI?
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/).

Cite this article

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  -