Beyond Besov spaces. I: Distributions of wavelet coefficients
type: Item
instance of: scholarly article
title: Beyond Besov spaces. I: Distributions of wavelet coefficients
zbMATH Open document ID: 1075.42014
author: Stéphane Jaffard
published in: The Journal of Fourier Analysis and Applications
publication date: 2005-02-11T00:00:00Z
review text: Wavelets are unconditional bases of Besov spaces \(B_p^{s,q}\), and the knowledge of Besov spaces to which a function \(f\) belongs can be deduced from the distribution of the wavelet coefficient of \(f\) at all scales. In the paper under review, the author considers the information that can be obtained from the distribution of wavelet coefficients at each scale, with independence of the wavelet. He shows that a convenient ``wavelet profile'', which is a function \(\nu_f(\alpha)\) that arises naturally in the multifractal analysis of random processes, gives more information than the knowledge of the Bessov spaces that contain \(f\). The results are tested by considering the wavelet profiles of some classical examples, such as Weierstrass functions and Brownian motions.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 26A30
zbMATH DE Number: 2133422
zbMATH Keywords: Besov spaces, multifractal formalism, oscillation spaces
zbMATH Keywords: wavelets
reviewed by: Joan Cerdà
MaRDI profile type: Publication
full work available at URL: s00041-004-0946-z
OpenAlex ID: W2089755390
DOI: 10.1007/S00041-004-0946-Z
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description: scientific article; zbMATH DE number 2133422