MATH 715 — Fall 1999
Fourier Analysis: Selected Topics in Harmonic Analysis

Instructor: Laurent Saloff-Coste

Time: MWF 10:10-11:00

Room: Malott 230

This course will treat different aspects of Fourier analysis. First, we will review some basic results concerning Fourier series (Chapter I of Katznelson). Then we will introduce the Fourier transform on Rⁿ (Chapter I of Stein-Weiss). We will discuss convolution, interpolation theorems between L^p spaces, Fourier multipliers and singular operators. Basic properties of harmonic polynomials and spherical harmonics will be developed (Chapter IV of Stein-Weiss). Other important results such that the Paley-Wiener theorem, Bochner's theorem, etc., will be treated together with some explicit applications.

The exact content of the course will partly depend on the audience interests.

Some references:

• E. Stein, Singular Integrals and Differentiability Properties of Functions, 1970, Princeton University Press.

• E. Stein and G. Weiss, Introduction to Fourier Analysis in Euclidean Spaces

• Y. Katznelson, An Introduction to Harmonic Analysis.

• G. Foland, A Course in Abstract Harmonic Analysis.

Last modified: April 7, 2003