Course Description

Topics

We will mainly cover the following standard topics:

• Locally convex spaces;
• Weak topologies; and
• Distributions.

If time permits, we will also cover the basics of the following special topic of applications:

• Weak convergence methods for variational problems of multiple integrals.

Textbook and References

For the standard topics, we will follow closely the textbook

• J. B. Conway, A Course in Functional Analysis, 2nd ed., Springer, 1990.

We will also occasionally consult the following references:

• J. Barros-Neto, An Introduction to the Theory of Distributions, Reprint ed., Krieger, 1981.
• W. Rudin, Functional Analysis, 2nd ed., McGraw-Hill, 1991.
• H. H. Schaefer and M. P. Wolff, Topological Vector Spaces,, 2nd ed., Springer, 1999.
• K. Yosida, Functional Analysis,, 6th ed., Springer, 2003.

Lecture notes on the special topic of applications will be distributed in the class.

Homework

There will be a few homework assignments.

Lecture Notes

Homework Assignments

Assignment 1 (pdf) - due Wednesday, January 24, 2007.

Assignment 2 (pdf) - due Wednesday, February 14, 2007.

Assignment 3 (pdf) - due Wednesday, March 14. February 7, 2007.

Last updated by Bo Li on January 26, 2007.