Course No. 827
Course title: Fourier analysis
Instructor: Andreas Seeger
Prerequisites: Basic real analysis
DESCRIPTION:
This is an introductory course into methods of Fourier analysis.
Topics include the basic theory of the Fourier transform, Fourier multipliers,
function spaces,
uncertainty principle, stationary phase method and oscillatory integrals,
Fourier restriction theorems and related topics.
If time permits we will also discuss geometric problems which can be
(partially) understood using Fourier analysis, such as the Falconer
distance problem.
Recommended text:
Thomas Wolff ``Lectures on Harmonic Analysis''.
Edited by Izabella Laba and Carol Shubin.
American Mathematical Society, University Lecture Series, vol. 29.
You may also download files
here .
More references:
J. Duoandikoetxea: Fourier Analysis
G. Folland: Real analysis
L. Grafakos: Classical and modern Fourier analysis
L. Hörmander: The analysis of linear partial differential operators, I.
W. Rudin: Functional analysis
E. Stein and G. Weiss: Introduction to Fourier analysis
on Euclidean spaces
E. Stein: Singular integral operators and differentiability
properties of functions.
E. Stein: Harmonic analysis.
Prof. Nazarov will give a
topics course (Math 828) in the spring semester of 2010.