### 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
.