Math 527/528
Functional Analysis
Gerald Folland
Autumn/Winter 2002-2003, Monday/Wednesday/Friday 11:30-12:20
Functional analysis is a huge subject, much too big to cover in two
quarters (or even two years), so this course will cover only selected
parts. Its focus will be the theory of linear operators on Banach spaces,
especially Hilbert spaces, and some of its applications. Spectral theory
will be a central theme, leading up to the spectral theorem for
self-adjoint operators, perhaps the most important and profound result of
the subject. There will be some emphasis on concrete examples arising from
differential and integral equations. The choice of topics will be guided
by the contents of Schechter's book, although I will not try to go through
the book page by page, and I will include a few things that aren't in it.
Text:
Principles of Functional Analysis (2nd ed) by Martin Schechter
(Amer Math Soc, 2001).
Prerequisites:
Real Analysis or Linear Analysis.