Harmonic Analysis

3 credits · Graduate School

Fourier series; Wiener's Lemma; Fourier integral; Plancherel Theorem; Haar measure on an LCA group G, Dual group and the Fourier integral; HausdorffYoung inequality; Hilbert transform; Hardy-Littlewood maximal functions; Marcinkiewicz Interpolation theorem; Singular integrals and the Calderon-Zygmund decomposition; multiresolution approximations; special topics from harmonic analysis, such as wavelets, frames, abstract harmonic analysis, symmetric spaces. Prerequisite: 6101. [3]