Math 725: A Second Course in Real Analysis

Spring 2017

Classes: 9:55 MWF, VV B337
Instructor: Andreas Seeger
Prerequisite: Undergraduate Analysis and Math 721

Office hour: Wednesday 2:30-3:30 p.m.
Course description:
I. Basic real analysis techniques (if not already covered in Math 721).
More on L^p and other spaces.
Some results on boundedness of linear operators
Interpolation of operators
II. Concepts in Functional Analysis (continuation):
Various function spaces
Compact operators
A version of the Spectral theorem
III. Distributions.
IV. Basic Fourier Analysis and Sobolev spaces.

We continue to use the Math 721 textbook: G. Folland: Real Analysis,
but there will be additional material.

Additional references: We rely on other sources, among them:
E.M. Stein, R. Shakarchi: Functional Analysis
W. Rudin: Functional analysis
E. M. Stein and G. Weiss: Introduction to Fourier analysis on Euclidean spaces
L. Hörmander: The analysis of linear partial differential operators I.
Sigurd Angenent's Math 725 Lecture notes .