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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.
List of contents
CAZAC sequences and Haagerup's characterization of cyclic N-roots.- Hardy spaces with variable exponents.- Regularity of maximal operators: recent progress and some open problems.- Gabor Frames: Characterizations and Coarse Structure.- On the approximate unit distance problem.- Hausdorff dimension, projections, intersections, and Besicovitch sets.- Dyadic harmonic analysis and weighted inequalities: the sparse revolution.- Sharp quantitative weighted BMO estimates and a new proof of the Harboure-Macías-Segovia's extrapolation theorem.- Lq dimensions of self-similar measures, and applications: a survey.- Sample paths properties of the set-indexed fractional Brownian motion.
