Continuation of Math 5051. The theory of integration in abstract and Euclidean spaces, and an introduction to the basic ideas of functional analysis. Math 5051-5052 forms the basis for the Ph.D. qualifying exam in analysis. Prereq: Math 417-418.
Topics we will cover:
Integration
Lp spaces
Differentiation
Distributions
Hilbert spaces
Spectral theory
There is no textbook. We will follow a set of notes which I will distribute periodically.