Recent developments in fractals and related fields

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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

Author(s): Zoltán Buczolich (auth.), Julien Barral, Stéphane Seuret (eds.)
Series: Applied and Numerical Harmonic Analysis
Edition: 1
Publisher: Birkhäuser Basel
Year: 2010

Language: English
Pages: 419
Tags: Geometry; Abstract Harmonic Analysis; Functional Analysis; Partial Differential Equations; Dynamical Systems and Ergodic Theory; Probability Theory and Stochastic Processes

Front Matter....Pages i-xx
Front Matter....Pages 1-1
Occupation Measure and Level Sets of the Weierstrass–Cellerier Function....Pages 3-18
Space-Filling Functions and Davenport Series....Pages 19-34
Dimensions and Porosities....Pages 35-43
On Upper Conical Density Results....Pages 45-54
On the Dimension of Iterated Sumsets....Pages 55-72
Geometric Measures for Fractals....Pages 73-89
Front Matter....Pages 91-91
A Walk from Multifractal Analysis to Functional Analysis with $${\mathcal{S}}^{\nu }$$ Spaces, and Back....Pages 93-106
Concentration of the Integral Norm of Idempotents....Pages 107-129
Le calcul symbolique dans certaines algèbres de type Sobolev....Pages 131-144
L p -Norms and Fractal Dimensions of Continuous Function Graphs....Pages 145-164
Uncertainty Principles, Prolate Spheroidal Wave Functions, and Applications....Pages 165-190
2-Microlocal Besov Spaces....Pages 191-201
Refraction on Multilayers....Pages 203-206
Wavelet Shrinkage: From Sparsity and Robust Testing to Smooth Adaptation....Pages 207-232
Front Matter....Pages 233-233
Simple Infinitely Ramified Self-Similar Sets....Pages 235-249
Quantitative Uniform Hitting in Exponentially Mixing Systems....Pages 251-266
Some Remarks on the Hausdorff and Spectral Dimension of V -Variable Nested Fractals....Pages 267-282
Cantor Boundary Behavior of Analytic Functions....Pages 283-294
Measures of Full Dimension on Self-Affine Graphs....Pages 295-308
Front Matter....Pages 309-309
A Process Very Similar to Multifractional Brownian Motion....Pages 311-326
Front Matter....Pages 309-309
Gaussian Fields Satisfying Simultaneous Operator Scaling Relations....Pages 327-341
On Randomly Placed Arcs on the Circle....Pages 343-351
T-Martingales, Size Biasing, and Tree Polymer Cascades....Pages 353-380
Front Matter....Pages 381-381
Univoque Numbers and Automatic Sequences....Pages 383-391
A Crash Look into Applications of Aperiodic Substitutive Sequences....Pages 393-399
Invertible Substitutions with a Common Periodic Point....Pages 401-409
Some Studies on Markov-Type Equations....Pages 411-419
Back Matter....Pages 421-422