Math 525B

Real Analysis

Math 525B the second semester in the graduate Real Analysis sequencer. The main topics are basic functional analysis, and examples of Banach and other topological vector spaces which are important in applications.


Folland: Real Analysis - Modern Techniques and Their Applications (Second Edition, 1999).

List of Topics:

Elements of Functional Analysis (Folland, Chapter 5)
Banach Spaces, Hahn-Banach Theorem and consequences, Baire Category - Open Mapping - Closed Graph Theorem, Uniform Boundedness Principle, Topological Vector Spaces (in particular Frechet and weak topologies), Hilbert spaces.

Lp spaces (mainly Folland, Chapter 6)
Basic inequalities and embeddings, Lp duality, Convolutions, Rearrangement inequalities, Hardy inequalities, Marcienkiewicz Interpolation Theorem, Calderon-Zygmund decomposition and their application to the Poisson equation.

Radon Measures
(Folland, 7.1-7.3)

Basic Distribution Theory

Haar Measures

Last modified: 2000/05/10
Marcel Oliver (