**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

**R**

^{d}(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.