Mathematics 541 (Harmonic Analysis I)

Fall 2010

Instructor: I. Laba (Math Bldg 200, 604-822-4457, ilaba(at)
Lectures: MWF 2-3, MATX 1102.
Office hours: M 12-1, F 1-2, and by appointment.

This course will provide an introduction to harmonic analysis on Euclidean spaces, with applications to number theory, PDE and geometric measure theory.

A list of topics we covered, with references to sources, is available here.

Homework assignments: Tentative topics:
Recommended textbooks:
Prerequisites: Basic real and functional analysis, including measure theory and integration, Banach spaces, linear operators, Lp spaces. Math 420/507 and 421/510 cover all the required background.

Your course grade will be based on 5 problem sets, tentatively due on September 24, October 8, October 27, November 17 and December 1. To allow for minor absences and short illnesses, the lowest score will be dropped; each of the remaining 4 problem sets will be worth 25% of your grade. There will be no final exam.

Math 542, offered in Spring 2011, will cover several current research areas in harmonic analysis and geometric measure theory. Tentatively, this will include Kakeya sets, restriction theory, maximal estimates and differentiation theorems for submanifolds of Rn, Hausdorff dimension and Fourier dimension (if this does not get covered in Math 541), Salem sets, projection theorems and distance sets.