| 02/02/2009: |
Point-set topology - topological spaces
|
| 04/04/2009: |
Point-set topology - continuity, product
topology
|
| 09/02/2009: |
Spaces of bounded and of continuous
functions, Urysohn's lemma; compact spaces
|
| 11/02/2009: |
Nets, Tychonoff's theorem
|
| 16/02/2009: |
Arzela-Ascoli theorem;
Banach spaces, the Hahn-Banach theorem
|
| 18/02/2009: |
Geometric forms of the Hahn-Banach
theorem; separation of convex subsets
|
| 23/02/2009: |
Baire category theorem, open mapping theorem
|
| 25/02/2009: |
Closed graph theorem; uniform boundedness
principle
|
| 02/03/2009: |
Topological vector spaces
|
| 04/03/2009: |
No class
|
| 09/03/2009: |
Weak topologies, the weak and the weak-*
topology; Banach-Alaoglu theorem
|
| 11/03/2009: |
Topologically complementary subspaces I
|
| 16/03/2009: |
Topologically complementary subspaces II
|
| 18/03/2009: |
Unbounded operators, adjoints, invertibility
|
| 20/03/2009: |
Midterm review
|
| 23/03/2009: |
Midterm Exam
|
| 25/03/2009: |
Extensions, closeable operators; examples of
differential operators
|
| 30/03/2009: |
No class
|
| 01/04/2009: |
No class
|
| 15/04/2009: |
Examples of differential operators and their
adjoints
|
| 17/04/2009: |
Introductory remarks on spectral theory;
definitions; 9:00 in Research I, 107
|
| 20/04/2009: |
Fredholm alternative
|
| 22/04/2009: |
Spectrum of a compact operator
|
| 24/04/2009: |
Lax-Milgram Theorem; residual spectrum,
self-adjoint operators;
spectral theorem for compact, self-adjoint
operators; 9:00 in Research I, 107
|
| 27/04/2009: |
Examples: Hilbert-Schmidt operators, inverses of
unbounded operators on a Gelfand-triple are compact
|
| 29/04/2009: |
Interlude: Introduction to Sobolov spaces
|
| 04/05/2009: |
Invertibility of unbounded operators revisited; the
spectrum of an unbounded operator
|
| 06/05/2009: |
Spectral mapping theorem
|
| 08/05/2009: |
Review for final exam 9:00 in
Research I, 107
|
| 11/05/2009: |
No class
|
| 13/05/2009: |
No class
|
| 20/05/2009: |
Final Exam, 8:00-10:00, East Hall 2
|