Jean Bourgain proved the decoupling inequality with Ciprian Demeter. Their theorem controls a function with Fourier support near a curved hypersurface through contributions from smaller frequency caps. The result connects curvature with improved summation estimates, with applications to restriction and Strichartz estimate for the free Schrödinger equation.[ref]
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Jean Bourgain was a renowned Belgian mathematician known for his significant contributions to various areas of mathematics, particularly in analysis, probability, and functional analysis. Born on February 28, 1954, and passing away on December 22, 2018, he was a professor at the Institute for Advanced Study in Princeton, New Jersey. Bourgain made groundbreaking advancements in topics such as harmonic analysis, partial differential equations, and high-dimensional geometry.