Prerequisite: Math 240AB or consent of instructor. It is assumed you have a strong background in undergraduate real analysis at the level of Rudin's "Principles of Mathematical Analysis", and have taken a graduate analysis class covering the first six chapters of Folland's "Real Analysis".
Course Description: Radon measures, Fourier transform and Fourier series, Distributions, Sobolev spaces. Additional topics as time permits.
Required Textbook: Real Analysis: Modern Techniques and Their Applications, second edition , by Gerald B. Folland; published by John Wiley & Sons, Inc.; 1999.
Recommended Textbooks: Analysis, second edition , by Elliot H. Lieb and Michael Loss; published by American Mathematical Society; 2001. (This is a good second text to read regarding distributions and Sobolev spaces with some applications to the calculus of variations.)Subject Material: We will cover material pertaining to Chapters 7-8 of Folland prior to the qual (first 5 weeks). Additional material relating to Fourier analysis and distributions will be presented after the qual as time permits.
Reading: Reading the textbook sections corresponding to the lecture schedule is considered part of the homework assignment. You are responsible for material in the assigned reading whether or not it is discussed in the lecture. It is assumed that you have read the corresponding material in advance of each lecture.