Recent Developments in Fractals and Related Fields (Applied and Numerical Harmonic Analysis)

The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scienti?c communities with s- ni?cant developments in harmonic analysis, ranging from abstract harmonic analysis to basic applications. The title of the series re?ects the importance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the int- leaving of theory and applications and their creative symbiotic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has ?o- ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilizationwith diverse areas. The intricate and f- damental relationship between harmonic analysis and ?elds such as signal processing, partial di?erential equations (PDEs), and image processing is - ?ected in our state-of-the-art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time-frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.

This book―an outgrowth of an international conference held in honor of Jacques Peyrière―provides readers with an overview of recent developments in the mathematical fields related to fractals. Included are original research contributions as well as surveys written by experts in their respective fields.

The chapters are thematically organized into five major sections:

• Geometric Measure Theory and Multifractals;

• Harmonic and Functional Analysis and Signal Processing;

• Dynamical Systems and Analysis on Fractals;

• Stochastic Processes and Random Fractals;

• Combinatorics on Words.

Recent Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenues for further research.

Contributors:

J.-P. Allouche, A.M. Atto, J.-M. Aubry, F. Axel, A. Ayache, C. Bandt, F. Bastin, P.R. Bertrand, A. Bonami, G. Bourdaud, Z. Buczolich, M. Clausel, Y. Demichel, X.-H. Dong, A. Durand, A.H. Fan, U.R. Freiberg, S. Jaffard, E. Järvenpää, A. Käenmäki, A. Karoui, H. Kempka, T. Langlet, K.-S. Lau, B. Li, M.M. France, S. Nicolay, E. Olivier, D. Pastor, H. Rao, S.Gy. Révész, J. Schmeling, A. Sebbar, P. Shmerkin, E.C. Waymire, Z.-X. Wen, Z.-Y. Wen, S.C. Williams, S. Winter