MATH 5140: Fourier Analysis
Description: Basic properties of Fourier series, convergence of Fourier series, applications of Fourier series. Fourier transform and distributions. Fourier transform in Lp-spaces. Hardy-Littlewood maximal inequality. Marcinkiewicz and Riesz-Thorin interpolation theorem. Hilbert and Riesz transforms, singular integrals, Calderon-Zygmund operators. Other topics in harmonic and Fourier analysis at the choice of the instructor (e.g. Littlewood-Paley theory, Marcinkiewicz multiplier theorem, fast Fourier transform, wavelets).
Prerequisites: MATH 5111.
Sections: Spring 2018 on Storrs Campus