New Trends in Applied Harmonic Analysis, Volume 2

1. Front Matter

   Pages i-xx

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2. CAZAC Sequences and Haagerup’s Characterization of Cyclic N-roots

   • John J. Benedetto, Katherine Cordwell, Mark Magsino

   Pages 1-43

3. Hardy Spaces with Variable Exponents

   • Víctor Almeida, Jorge J. Betancor, Estefanía Dalmasso, Lourdes Rodríguez-Mesa

   Pages 45-67

4. Regularity of Maximal Operators: Recent Progress and Some Open Problems

   • Emanuel Carneiro

   Pages 69-92

5. Gabor Frames: Characterizations and Coarse Structure

   • Karlheinz Gröchenig, Sarah Koppensteiner

   Pages 93-120

6. On the Approximate Unit Distance Problem

   • Alex Iosevich

   Pages 121-128

7. Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets

   • Pertti Mattila

   Pages 129-157

8. Dyadic Harmonic Analysis and Weighted Inequalities: The Sparse Revolution

   • María Cristina Pereyra

   Pages 159-239

9. Sharp Quantitative Weighted \(\mathop {\mathrm {BMO}}\) Estimates and a New Proof of the Harboure–Macías–Segovia’s Extrapolation Theorem

   • Alberto Criado, Carlos Pérez, Israel P. Rivera-Ríos

   Pages 241-256

10. \(L^q\) Dimensions of Self-similar Measures and Applications: A Survey

    • Pablo Shmerkin

    Pages 257-292

11. Sample Paths Properties of the Set-Indexed Fractional Brownian Motion

    • Erick Herbin, Yimin Xiao

    Pages 293-316

12. Back Matter

    Pages 317-321

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This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include:

• Gabor frames
• Falconer distance problem
• Hausdorff dimension
• Sparse inequalities
• Fractional Brownian motion
• Fourier analysis in geometric measure theory

This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.

• Harmonic Analysis math
• Harmonic Analysis book
• Harmonic Analysis trends
• Applied harmonic analysis
• Geometric measure theory book
• Signal processing math
• Image processing math
• Ursula Molter mathematics
• CIMPA Research School
• CIMPA 2017 school

• Vanderbilt University, Nashville, USA

  Akram Aldroubi

• Department of Mathematics (FCEyN), Universidad de Buenos Aires, Buenos Aires, Argentina

  Carlos Cabrelli, Ursula Molter

• Department of Mathematics (LAMA), Université Paris-Est Créteil, Creteil, France

  Stéphane Jaffard

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