Description

Harmonic analysis on Euclidean spaces is a large field of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the investigation of and generalization of the notions of Fourier series and Fourier transforms - an extended formulation of Fourier analysis. This graduate special topics course will concentrate on the real variable methods of the theory, and provide a solid background for other courses including PDE. Below is a sample of topics covered in the course:

• L^p spaces and interpolation; Hardy-Littlewood maximal function; Fourier transform and distributions; Singular integrals of convolution type; Littlewood-Paley theory and multipliers; Smoothness and function spaces; Dirichlet problem for elliptic equations.

Prerequisites

Solid backgrounds in real and functional analysis as well as measures and integrals.

Texts

• Classical and Modern Fourier Analysis by Loukas Grafakos, Pearson Education, Inc. 2004.
• Lecture Notes: Harmonic Analysis by Russell Brown, University of Kentucky, 2015.