Prevalent mixed Hölder spectra and mixed multifractal formalism in a product of continuous Besov spaces. (21st July 2017)

• Record Type: Journal Article
• Authors: Ben Abid, Moez
• Is Part Of: Nonlinearity. Volume 30:Number 8(2017:Aug.)
• Page Start: 3332
• Page End: 3348
• Publication Date: 2017-07-21
• Subjects: Besov spaces -- wavelet leaders -- prevalence -- singularity spectrum; 26A16 -- 26A30 -- 28A78 -- 28A80 -- 37C20 -- 42C40 -- 46E35 -- 54C50 -- 65T60; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa79c7
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this work we show that the mixed Hölder spectra of a pair of functions in a prevalent set of a product of continuous Besov spaces satisfies a mixed multifractal formalism based on the wavelet leaders. The results can be easily extended for finitely many functions in a product of continuous Besov spaces. We will use the notion of the essential shyness to calculate the mixed wavelet leaders scaling function for almost every pair of functions. As far as we know this is the first application of this notion.