Enno Lenzmann MIT, Department of Mathematics Room 2-378 Email: lenzmann at math.mit.edu Office hours: Wed, 3-4pm, Room 2-378.
Time and Place:
Monday, Wednesday, and Friday, 10-11:00am. Room 2-102
Room 2-131
Outline of the Course
This course provides a thorough introduction to Fourier Analysis and it is designed for students with a profound knowledge of undergraduate analysis. The tentative outline is as follows.
Basic properties of Fourier series.
Lebesgue measure and integration; Lp and Hilbert spaces.
Convergence theorems for Fourier series.
Applications: Heat equation on the circle and isoperimetric inequality.
Fourier transform on d-dimensional Euclidean space
Applications: Heat and Schroedinger's equation
Sobolev spaces and inequalities
Distributions and Fourier Transform
Textbook
E. M. Stein and S. Shakarchi: Fourier Analysis: An Introduction. Princeton University Press (2003) Further suggested reading on integration and measure theory are: M. Adams and V. Gulllemin "Measure Theort and Probability" as well as Chapter 11 (on Lebesgue Integration) in W. Rudin "Principles of Mathematical Analysis"
Homework and Exams
There will be weekly homework assignments (except for weeks having midterms) and three midterms. For your final grade, homework and midterms count each 50 percent. There will be no final exam.