Mathematical Sciences: Fourier Analysis

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Wainger/Seeger DMS-9501040 The proposed research will deal with several problems in classical analysis related to integral operators, Fourier integral operators, averages over curves and surfaces, maximal functions, functions of the Laplacian on Riemannian manifolds, and the interrelation between these topics. Mathematical research in harmonic analysis seeks to study the fine structure of mathematical functions and their underlying domains of definition. The tools developed by this work bring out hidden relationships not ordinarily detected by more classical methods.