Recent Developments in Fractals and Related Fields

By: Julien Barral (Editor), Stephane Seuret (Editor)

Hardcover | 12 August 2010

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This book-an outgrowth of an international conference held in honor of Jacques Peyriere-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. Jarvenpaa, A. Kaenmaki, A. Karoui, H. Kempka, T. Langlet, K.-S. Lau, B. Li, M. Mendes France, S. Nicolay, E. Olivier, D. Pastor, H. Rao, S.Gy. Revesz, J. Schmeling, A. Sebbar, P. Shmerkin, E.C. Waymire, Z.-X. Wen, Z.-Y. Wen, S.C. Williams, S. Winter

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ANHA Series Preface	p. VII
Preface	p. XI
Geometric Measure Theory and Multifractals
Occupation Measure and Level Sets of the Weierstrass-Cellerier Function	p. 3
Space-Filling Functions and Davenport Series	p. 19
Dimensions and Porosities	p. 35
On Upper Conical Density Results	p. 45
On the Dimension of Iterated Sumsets	p. 55
Geometric Measures for Fractals	p. 73
Harmonic and Functional Analysis and, Signal Processing
A Walk from Multifractal Analysis to Functional Analysis with S Spaces, and Back	p. 93
Concentration of the Integral Norm of Idempotents	p. 107
Le calcul symbolique dans certaines algébres de type Sobolev	p. 131
L^p-Norms and Fractal Dimensions of Continuous Function Graphs	p. 145
Uncertainty Principles, Prolate Spheroidal Wave Functions, and Applications	p. 165
2-Microlocal Besov Spaces	p. 191
Refraction on Multilayers	p. 203
Wavelet Shrinkage: From Sparsity and Robust Testing to Smooth Adaptation	p. 207
Dynamical Systems and Analysis on Fractals
Simple Infinitely Ramified Self-Similar Sets	p. 235
Quantitative Uniform Hitting in Exponentially Mixing Systems	p. 251
Some Remarks on the Hausdorff and Spectral Dimension of V-Variable Nested Fractals	p. 267
Cantor Boundary Behavior of Analytic Functions	p. 283
Measures of Full Dimension on Self-Affine Graphs	p. 295
Stochastic Processes and Random Fractals
A Process Very Similar to Multifractional Brownian Motion	p. 311
Gaussian Fields Satisfying Simultaneous Operator Scaling Relations	p. 327
On Randomly Placed Arcs on the Circle	p. 343
T-Martingales, Size Biasing, and Tree Polymer Cascades	p. 353
Combinatorics on Words
Univoque Numbers and Automatic Sequences	p. 383
A Crash Look into Applications of Aperiodic Substitutive Sequences	p. 393
Invertible Substitutions with a Common Periodic Point	p. 401
Some Studies on Markov-Type Equations	p. 411
Table of Contents provided by Ingram. All Rights Reserved.

Recent Developments in Fractals and Related Fields

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