Monday, January 27, 2014

Course Information

Time and Place: TTh 10:30–11:45 in MATH 215

Instructor: Arshak Petrosyan
Office Hours: TTh 1:30–2:30pm, or by appointment, in MATH 610

Textbook: E.M. Stein & R. Shakarchi, Fourier Analysis: An Introduction, Princeton University Press, 2003.

Syllabus is essentially the first six chapters in [Stein-Shakarchi]:
1. The Genesis of Fourier Analysis
2. Basic Properties of Fourier Series
3. Convergence of Fourier Series
4. Some Applications of Fourier Series
5. The Fourier Transform on R
6. The Fourier Transform on Rd (excluding the higher dimensional wave equation)

Particlular topics include: Fourier series, uniqueness, convolutions, good kernels, Cesaro and Abel summation, Fejer and Poisson kernels, Parseval's identity, Fourier transform, Schwarz class, Gaussian kernels, Plancherel's identity, Poisson summation formula, Radon transform; applications to the wave, heat, and Laplace equations, the isoperimetric inequality, equidistribution theorems.

Homework will be collected weekly on Thursdays. The assignments will be posted on this website at least one week prior to due date.

Exams: There will be two midterm exams and a final exam (project). Exact times will be specified in due course.