Instructor: | Marcel Oliver |
Email: | m.oliver@jacobs-university.de |
Phone: | 200-3212 |
Office hours: | Mo, Fr 10:00 in Research I, 107 |
Grader: | Mahmut Çalik |
Email: | m.calik@jacobs-university.de |
Lectures: | We 11:15, Fr 9:45 in East Hall 3 |
Homework: | 30% |
Midterm Exam: | 30% |
Final Exam: | 40% |
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 |