Multifractal analysis of rectangular pointwise regularity with hyperbolic wavelet bases
type: Item
instance of: scholarly article
title: Multifractal analysis of rectangular pointwise regularity with hyperbolic wavelet bases
zbMATH Open document ID: 1484.42030
author: Moez Ben Abid
author: Mourad Ben Slimane
author: Ines Ben Omrane
author: Maamoun Turkawi
published in: The Journal of Fourier Analysis and Applications
publication date: 2021-12-08T00:00:00Z
review text: The paper deals with the analysis of directional or anisotropic features for multidimensional signals. The authors define rectangular pointwise regularity through local oscillations of the function over rectangular parallelepipeds. To characterize anisotropic properties of sets the notion of the dimension print is used. It is a set of positive vectors depending on a behavior of some Hausdorf-type measure along different directions. The authors characterize rectangular pointwise regularity in terms of hyperbolic wavelet coefficients and wavelet leaders. The hyperbolic wavelet basis consists of products of shifts and dyadic dilations of one dimension \(r\)-regular wavelet functions and scaling functions that corresponds to diagonal extension matrix with \(2\)'s on the main diagonal and a separable MRA. The authors obtain a numerical procedure that yields information on the dimension print of sets of level rectangular pointwise regularities, expressed in terms of hyperbolic wavelet leaders. An example of anisotropic selfsimilar cascade wavelet series is given, where the anisotropy corresponds to a Sierpinski carpet.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 7441169
zbMATH Keywords: pointwise regularity
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: dimension print
zbMATH Keywords: wavelet analysis
zbMATH Keywords: anisotropic selfsimilar cascade wavelet series
reviewed by: Elena Lebedeva
MaRDI profile type: Publication
full work available at URL: s00041-021-09890-7
OpenAlex ID: W3214644575
Wikidata QID: Q115609267
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DOI: 10.1007/S00041-021-09890-7
description: scientific article; zbMATH DE number 7441169