Math 828, Harmonic Analysis


Instructor: Serguei Denissov, 623 VV.
Lectures:       TTh, 2:30-3:45, B325    
Office hours: by appointment
Grading:        the grade will be based on your participation.
If time permits, student volunteers will have a chance to give a presentation on some topics.


We will cover some classic and very recent delelopments in Harmonic Analysis. This might include topics such as: Carleson theorem on a.e. convergence of Fourier series (solution to Lusin's conjecture), polynomials method and its applications, decoupling theorem of Bourgain and Demeter, wave packet decompositions and applications to PDE.

Additional reading (this list will be populated as we progress with the material).

Rough plan of lectures:

1. Menchoff-Rademacher theorem, some orthonormal systems.
2. Rademacher system, a.e. convergence and divergence.
3. Kolmogorov's theorem about a.e. divergent series for summable function (random construction).
4. Polynomial method: some examples (check, e.g.,
5. Carleson theorem.