New Trends in Applied Harmonic Analysis, Volume 2 - Harmonic Analysis, Geometric Measure Theory, and Applications

Description

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. Front Matter ....Pages i-xx CAZAC Sequences and Haagerup’s Characterization of Cyclic N-roots (John J. Benedetto, Katherine Cordwell, Mark Magsino)....Pages 1-43 Hardy Spaces with Variable Exponents (Víctor Almeida, Jorge J. Betancor, Estefanía Dalmasso, Lourdes Rodríguez-Mesa)....Pages 45-67 Regularity of Maximal Operators: Recent Progress and Some Open Problems (Emanuel Carneiro)....Pages 69-92 Gabor Frames: Characterizations and Coarse Structure (Karlheinz Gröchenig, Sarah Koppensteiner)....Pages 93-120 On the Approximate Unit Distance Problem (Alex Iosevich)....Pages 121-128 Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets (Pertti Mattila)....Pages 129-157 Dyadic Harmonic Analysis and Weighted Inequalities: The Sparse Revolution (María Cristina Pereyra)....Pages 159-239 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 \(L^q\) Dimensions of Self-similar Measures and Applications: A Survey (Pablo Shmerkin)....Pages 257-292 Sample Paths Properties of the Set-Indexed Fractional Brownian Motion (Erick Herbin, Yimin Xiao)....Pages 293-316 Back Matter ....Pages 317-321