This is the second part of a year-long graduate course on an introduction to
We will mainly cover the following standard topics:
If time permits, we will also cover the basics of the following special topic of applications:
- Locally convex spaces;
- Weak topologies; and
- Weak convergence methods for variational problems of multiple integrals.
Textbook and References
For the standard topics, we will follow closely the textbook
We will also occasionally consult the following references:
J. B. Conway, A Course in Functional Analysis, 2nd ed., Springer, 1990.
Lecture notes on the special topic of applications will be distributed in the class.
- 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.
There will be a few homework assignments.
Weak convergence methods for energy minimization
- Assignment 1
- due Wednesday, January 24, 2007.
- Assignment 2
- due Wednesday, February 14, 2007.
- Assignment 3
- due Wednesday, March 14. February 7, 2007.
Last updated by Bo Li on January 26, 2007.