Summary: MATH 757: Fourier Analysis (Spring 2012)
MWF 9:00-9:50 Minard 336
Instructor: Maria Alfonseca
Office: Minard 412B
Office Hours: MWF 10:00-11:30 am and by appointment. Please talk to me after class or
send me an e-mail to set up appointments.
Text: Fourier Analysis, an introduction) by E.M. Stein and R. Shakarchi, Princeton University
Topics: Fourier Analysis arose in the XIX century as a method to solve the heat and the wave
equations, two of the most representative second order partial differential equations. It requires
to decompose a function as an infinite sum of trigonometric functions, and thus immediately
introduced the problem of studying which functions can be written in this way, and in which
sense the trigonometric series is convergent. In this course we will study these representation
and convergence problems, and some applications. Fourier analysis has proven useful not only
for PDEs, but also in functional analysis, geometry (tomography) and number theory.
Attendance: Attendance is expected and required. There will be weekly student presen-
tations. You are responsible for all the material covered in class and all the assignments and
announcements made. If you need to miss class due to sickness or other reason, please email me.