Recent Developments in Fractals and Related Fields

1. Front Matter

   Pages i-xx

   PDF

2. Geometric Measure Theory and Multifractals

   1. Front Matter

      Pages 1-1

      PDF

   2. Occupation Measure and Level Sets of the Weierstrass–Cellerier Function

      • Zoltán Buczolich

      Pages 3-18

   3. Space-Filling Functions and Davenport Series

      • Stéphane Jaffard, Samuel Nicolay

      Pages 19-34

   4. Dimensions and Porosities

      • Esa Järvenpää

      Pages 35-43

   5. On Upper Conical Density Results

      • Antti Käenmäki

      Pages 45-54

   6. On the Dimension of Iterated Sumsets

      • Jörg Schmeling, Pablo Shmerkin

      Pages 55-72

   7. Geometric Measures for Fractals

      • Steffen Winter

      Pages 73-89

3. Harmonic and Functional Analysis and, Signal Processing

   1. Front Matter

      Pages 91-91

      PDF

4. Harmonic and Functional Analysis and Signal Processing.

   1. A Walk from Multifractal Analysis to Functional Analysis with \({\mathcal{S}}^{\nu }\) Spaces, and Back

      • Jean-Marie Aubry, Françoise Bastin

      Pages 93-106

   2. Concentration of the Integral Norm of Idempotents

      • Aline Bonami, Szilárd Gy. Révész

      Pages 107-129

   3. Le calcul symbolique dans certaines algèbres de type Sobolev

      • Gérard Bourdaud

      Pages 131-144

   4. L ^p-Norms and Fractal Dimensions of Continuous Function Graphs

      • Yann Demichel

      Pages 145-164

   5. Uncertainty Principles, Prolate Spheroidal Wave Functions, and Applications

      • Abderrazek Karoui

      Pages 165-190

   6. 2-Microlocal Besov Spaces

      • Henning Kempka

      Pages 191-201

   7. Refraction on Multilayers

      • Michel Mendès France, Ahmed Sebbar

      Pages 203-206

   8. Wavelet Shrinkage: From Sparsity and Robust Testing to Smooth Adaptation

      • Dominique Pastor, Abdourrahmane M. Atto

      Pages 207-232

5. Dynamical Systems and Analysis on Fractals

   1. Front Matter

      Pages 233-233

      PDF

6. Dynamical Systems and Analysis on Fractals.

   1. Simple Infinitely Ramified Self-Similar Sets

      • Christoph Bandt

      Pages 235-249

   2. Quantitative Uniform Hitting in Exponentially Mixing Systems

      • Ai Hua Fan, Thomas Langlet, Bing Li

      Pages 251-266

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.

• Brownian motion
• Martingale
• analysis on fractals
• combinatorics on words
• ergodic theory and dynamical systems
• fractional Brownian motion
• functional analysis
• geometric measure theory
• harmonic analysis
• linear optimization
• mixing
• stochastic process
• stochastic processes

• Département de Mathématiques, LAGA (UMR CNRS 7539), Villetaneuse, France

  Julien Barral

• Université Paris-Est, Laboratoire d'Analyse et de Mathématique, CRETEIL Cedex, France

  Stéphane Seuret

Policies and ethics