Recent Developments in Fractals and Related Fields

Editors:

ISBN: 978-0-8176-4887-9 (Print) 978-0-8176-4888-6 (Online)

Table of contents (27 chapters)

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  1. Front Matter

    Pages i-xx

  2. Geometric Measure Theory and Multifractals

    1. Front Matter

      Pages 1-1

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      Book Chapter

      Pages 3-18

      Occupation Measure and Level Sets of the Weierstrass–Cellerier Function

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      Book Chapter

      Pages 19-34

      Space-Filling Functions and Davenport Series

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      Book Chapter

      Pages 35-43

      Dimensions and Porosities

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      Book Chapter

      Pages 45-54

      On Upper Conical Density Results

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      Book Chapter

      Pages 55-72

      On the Dimension of Iterated Sumsets

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      Book Chapter

      Pages 73-89

      Geometric Measures for Fractals

  3. Harmonic and Functional Analysis and Signal Processing.

    1. Front Matter

      Pages 91-91

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      Book Chapter

      Pages 93-106

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

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      Book Chapter

      Pages 107-129

      Concentration of the Integral Norm of Idempotents

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      Book Chapter

      Pages 131-144

      Le calcul symbolique dans certaines algèbres de type Sobolev

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      Book Chapter

      Pages 145-164

      L p -Norms and Fractal Dimensions of Continuous Function Graphs

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      Book Chapter

      Pages 165-190

      Uncertainty Principles, Prolate Spheroidal Wave Functions, and Applications

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      Book Chapter

      Pages 191-201

      2-Microlocal Besov Spaces

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      Book Chapter

      Pages 203-206

      Refraction on Multilayers

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      Book Chapter

      Pages 207-232

      Wavelet Shrinkage: From Sparsity and Robust Testing to Smooth Adaptation

  4. Dynamical Systems and Analysis on Fractals.

    1. Front Matter

      Pages 233-233

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      Book Chapter

      Pages 235-249

      Simple Infinitely Ramified Self-Similar Sets

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      Book Chapter

      Pages 251-266

      Quantitative Uniform Hitting in Exponentially Mixing Systems

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      Book Chapter

      Pages 267-282

      Some Remarks on the Hausdorff and Spectral Dimension of V-Variable Nested Fractals

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      Book Chapter

      Pages 283-294

      Cantor Boundary Behavior of Analytic Functions

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      Book Chapter

      Pages 295-308

      Measures of Full Dimension on Self-Affine Graphs

  5. Stochastic Processes and Random Fractals

    1. Front Matter

      Pages 309-309

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      Book Chapter

      Pages 311-326

      A Process Very Similar to Multifractional Brownian Motion

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