This Issue


Fractals: Vol. 24, No. 04
Print ISSN: 0218-348X
Online ISSN: 1793-6543

 
2016 Impact Factor
1.540
writing-guides   ealerts
Connect with WS
 

Fractals

Complex Geometry, Patterns, and Scaling in Nature and Society




MIXED MULTIFRACTAL ANALYSIS FOR FUNCTIONS: GENERAL UPPER BOUND AND OPTIMAL RESULTS FOR VECTORS OF SELF-SIMILAR OR QUASI-SELF-SIMILAR OF FUNCTIONS AND THEIR SUPERPOSITIONS

MOURAD BEN SLIMANE*, §
ANOUAR BEN MABROUK
JAMIL AOUIDI

*King Saud University, Department of Mathematics, College of Science, P. O. Box 2455, Riyadh 11451, Saudi Arabia

Faculty of Sciences of Monastir, Department of Mathematics, Computational Mathematics Laboratory, 5019, Monastir, Tunisia

Department of Mathematics, Preparatory Institute for Military Academies, Fondouk Jedid, 8012 Nabeul, Tunisia

§Corresponding author.

Received: January 18, 2016
Accepted: May 17, 2016
Published: August 31, 2016

Mixed multifractal analysis for functions studies the Hölder pointwise behavior of more than one single function. For a vector F = (f1,,fL) of L functions, with L 2, we are interested in the mixed Hölder spectrum, which is the Hausdorff dimension of the set of points for which each function fl has exactly a given value αl of pointwise Hölder regularity. We will conjecture a formula which relates the mixed Hölder spectrum to some mixed averaged wavelet quantities of F. We will prove an upper bound valid for any vector of uniform Hölder functions. Then we will prove the validity of the conjecture for self-similar vectors of functions, quasi-self-similar vectors and their superpositions. These functions are written as the superposition of similar structures at different scales, reminiscent of some possible modelization of turbulence or cascade models. Their expressions look also like wavelet decompositions.

Keywords: Hölder Regularity; Hausdorff Dimension; Mixed Multifractal Formalism; Wavelets; Self-Similar Vectors of Functions; Quasi-Self-Similar Vectors of Functions; Superpositions
Cited by (1):
, , , . (2017) Mixed Wavelet Leaders Multifractal Formalism in a Product of Critical Besov Spaces. Mediterranean Journal of Mathematics 14:4. Online publication date: 1-Aug-2017. [Crossref]

Remember to check out the Most Cited Articles in FNL !

Check out books on Fractals
Includes authors Benoit Mandelbrot, Michael Frame, Nathan Cohen, Susie Vrobel and more