Dato | Undervises av | Sted | Tema | Kommentarer / ressurser |
21.08.2007 | Nadia S. Larsen | B 70 | 1.1-1.4 | Normerte rom. Kvotientrom. |
22.08.2007 | Nadia S. Larsen | B 70 | 1.5, 2.1a - 2.1d | Komplettering av normerte rom. Hilbertrom. |
28.08.2007 | Nadia S. Larsen | B 70 | 1.5, 2.1a; Exercises (updated list). | Completion of a normed space; Hilbert spaces; Exercises: chapter 1: 1, 11, 18, 20, 22, 23;. |
29.08.2007 | Nadia S. Larsen | 2.1b - 2.1e; 2.2a - 2.2b | Bessel's inequality, Gram-Schmidt orthogonalisation, Parseval's identity, Projection onto a subspace | |
04.09.2007 | Sections 2.1e, 2.2a-b. Exercises | Parseval's identity. Distance to a convex set. Projection onto a subspace.Chapter 2: exercises 1, 3, 5, 8b. | ||
05.09.2007 | Sections 2.2c, 2.3a-b. | Orthogonal decomposition in Hilbert spaces. Linear functionals. | ||
11.09.2007 | Sections 2.3c, 3.1.a. Exercises | Riesz Representation Theorem for a Hilbert space. Examples of linear functionals. The Hahn-Banach theorem and some of its corollaries.Chapter 2: exercises: 11, 14, 15, 16. | ||
12.09.2007 | Sections 3.1a, 3.2 | Corollaries of the Hahn-Banach theorem. Examples of dual spaces. | ||
18.09.2007 | NSL | Sections 3.1a, 3.2, 4.1. Exercises | The annihilator of a subspace. Examples of reflexive spaces. Bounded linear operators.Chapter 3: exercises 2, 3, 4, 5. | |
19.09.2007 | NSL | Sections 4.2, 4.3 a | Examples of linear operators. Compact sets. Compact operators: first properties. | |
25.09.2007 | NSL | B70 | Sections 4.2, 4.3a. Exercises | Some examples of linear operators. Compact sets. Chapter 3, exercise 8. Chapter 4, exercises 1, 2a. |
26.09.2007 | NSL | B70 | Sections 4.3b, 4.4 | Compact operators. Dual operators. |
02.10.2007 | NSL | B70 | Section 4.5. Exercises | Operators of finite rank.Chapter 4, exercises 2b, 5, 6, 7. |
03.09.2007 | NSL | B70 | Sections 4.5a, 4.6, 4.7 | Examples of compact operators. Modes of convergence in L(X). |
09.10.2007 | NSL | B70 | Sections 4.5a, 5.1. Exercises | The integral operator in L2. Spectrum of an operator.Chapter 4: exercises 10, 11, 15, 21, 23. |
10.10.2007 | NSL | B70 | Section 5.2 | Fredholm theory for compact operators on Banach spaces |
16.10.2007 | NSL | B70 | Section 5.2, Exercises | Fredholm theory of compact operatorsChapter 4, exercise 9. Chapter 5, exercises 1, 3, 11 |
17.10.2007 | NSL | B70 | Section 5.2 | Fredholm theory of compact operators |
23.10.2007 | NSL | B70 | Section 6.1-6.2, Exercises | Spectral theory for compact self-adjoint operatorsChapter 5, exercise 9. |
24.10.2007 | NSL | B70 | Section 6.2, 6.3 | Spectral theory of compact self-adjoint operators, minimax principle, positive operators. |
30.10.2007 | NSL | B70 | Section 6.2c, 6.3, Exercises | The second Hilbert-Schmidt theorem. Positive operators. Chapter 6, exercise 1, 3a-c. |
31.10.2007 | NSL | B70 | Section 6.3, 6.4 | Ordering in the space of self-adjoint operators. Projections. |
06.11.2007 | NSL | B70 | Exercises. Sections 6.4 and 7.0. | Exercises 1, 3a-c, chapter. 6. Self-adjoint projections. Functional calculus |
07.11.2007 | NSL | B70 | Sections 7.0, 7.1 a. | Functional calculus (continued) |
13.11.2007 | No lectures this week | |||
14.11.2007 | No lectures this week | |||
20.11.2007 | NSL | B70 | Section 7.1b | Spectral integral |
21.11.2007 | NSL | B70 | Sections 7.2, 7.3 | Spectral theorem for bounded self-adjoint operators |
27.11.2007 | NSL | B70 | Sections 7.3, 7.4 | Spectral family. Spectrum of a self-adjoint operator. |
28.11.2007 | NSL | B70 | Open session (questions), Exercises 1, 2, in chapter 7. |
Undervisningsplan
Publisert 12. juni 2007 16:47
- Sist endret 27. nov. 2007 16:54