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Mathematical Analysis

Harmonic analysis is a corner stone in the solution of many problems coming from the natural and social sciences. The analysis group at the ICMAT works actively on directional maximal operators, convergence of Fourier series and integrals, noncommutative Calderón-Zygmund theory, harmonic analysis on discrete groups, restriction of the Fourier transform to surfaces, inverse problems, geometric measure theory and weighted norm inequalities. These areas have applications in the recovery of potentials from scattered plane waves, elliptic and dispersive partial differential equations, number theory, as well as quantum probability and quantum information theory.