Mathematics 541: Harmonic Analysis, Fall 2005

MWF 11-12, MATX 1102

Instructor: I. Laba.
Office: Math Bldg 239.
Phone: 822 2450.
E-mail: ilaba(at)
Office hours: Mon 3-4, Tue 11-12, Fri 10-11.

Homework 1, due on Friday, October 7
Homework 2, due on Friday, November 18

This course will provide an introduction to Euclidean harmonic analysis as a whole, followed by a closer look at selected areas of current research, with particular focus on the Kakeya and restriction problems. The latter are central problems in harmonic analysis which have also been linked to deep questions in number theory and combinatorics, and which have (at least indirectly) stimulated the recent exciting developments related to Szemer\'edi's theorem on arithmetic progressions. The goal is to provide a good foundation for further reading and research, with technicalities kept to a minimum. I hope that the course will be accessible and interesting to students with a variety of backgrounds.

Tentative outline:

Prerequisites: Completion of Math 420/507 and 421/510, or equivalent familiarity with basic real and functional analysis. Many essential analysis topics are usually not included in Math 507 and 510: Riesz representation theorem, Sobolev spaces, distributions, interpolation, operator theory (eg. dual and unitary operators), to name just a few. Such topics will be introduced as needed - typically, I will only state the required results without proof.

Textbook: T. Wolff, Lectures on Harmonic Analysis, AMS 2003.

Additional resources: