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
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
- Basic Distribution Theory
- Haar Measures
Last modified: 2000/05/10