NDLI: Mixed Wavelet Leaders Multifractal Formalism for Baire Generic Functions in a Product of Intersections of Hölder Spaces with Non-Continuous Besov Spaces

Content Provider	Springer Nature Link
Author	Ben Abid, Moez Ben Slimane, Mourad Ben Omrane, Ines
Copyright Year	2016
Abstract	In Ben Slimane (Mediterr J Math, 13(4):1513–1533 (2016)), the second author proved that, generically in the Baire category sense, pairs of functions in $${B_{t_{1}}^{s_{1},\infty}(\mathbb{R}^m) \times B_{t_{2}}^{s_{2},\infty}(\mathbb{R}^m) }$$ , for $${s_{1} > \frac{m}{t_{1}}}$$ and $${s_{2} > \frac{m}{t_{2}}}$$ , satisfy a mixed multifractal formalism based on wavelet leaders. In this paper, we extend this validity on $${(B_{t_{1}}^{s_{1},\infty}(\mathbb{R}^m) \cap C^{\gamma_{1}}(\mathbb{R}^m)) \times (B_{t_{2}}^{s_{2},\infty}(\mathbb{R}^m) \cap C^{\gamma_{2}}(\mathbb{R}^m)}$$ , for $${0 < \gamma_{1} < s_{1} < \frac{m}{t_{1}}}$$ and $${0 < \gamma_{2} < s_{2} < \frac{m}{t_{2}}}$$ . The main change is that the wavelet coefficients of the saturating function which generates the residual $${G_\delta}$$ set are not everywhere large enough and do not coincide everywhere with the wavelet leaders. Nevertheless, the computation of the wavelet leaders is done everywhere and allows to deduce both mixed spectra and mixed scaling function.
Ending Page	5118
Page Count	26
Starting Page	5093
File Format	PDF
ISSN	16605446
e-ISSN	16605454
Journal	Mediterranean Journal of Mathematics
Issue Number	6
Volume Number	13
Language	English
Publisher	Springer International Publishing
Publisher Date	2016-09-20
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Singular functions, Cantor functions, functions with other special properties Hölder exponent Hausdorff dimension Baire category multifractal Fractals Mathematics Baire category, Baire spaces wavelet leaders Wavelets and other special systems Hausdorff and packing measures
Content Type	Text
Resource Type	Article
Subject	Mathematics

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