| 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