MATH 6110 - Real Analysis

Camil Muscalu, fall 2014.

This is one of our core courses in the graduate program. For the fall 2014 class, we plan to use a combination of three books by Stein and Shakarchi, devoted to Real, Fourier and Functional Analysis.

The main topics will include:

1. Measures and abstract integration.
2. Lebesgue measure, L^p spaces.
3. Hilbert spaces, Banach spaces.
4. Fourier series. (Optional: Fourier transforms, Fourier inversion, and Plancherel theorems)
5. Differentiation.
6. Integration on product spaces, Fubini’s theorem.