725 - Second Course in Real Analysis

This is the second course in the graduate analysis sequence designed to prepare the students for qualifying exams.
The topics will include Fourier transform, distributions, Sobolev imbedding theorems, more on Banach and Hilbert spaces,
and additional topics as time allows (such as for example Hausdorff measures and fractals or spectral theorem for self-adjoint
operators and applications to Schrodinger equations).
The main texts for the course will be
Lieb and Loss, "Analysis" and Stein and Shakarchi, "Functional Analysis: Introduction to further topics in Analysis".
Other useful texts include
Stein and Shakarchi, "Real analysis: Integration, measure theory and Hilbert spaces"
Brezis, "Functional analysis, Sobolev spaces and partial differential equations"