| Date | Teacher | Place | Topic | Lecture notes / comments |
| 25.08.2008 | Nadia S. Larsen (NL)? | B71? | Prerequisites (Sections 1.2-1.3)? | Review of basic notions from metric spaces. Short overview of the theory of Lebesgue integration. ? |
| 26.08.2008 | NL? | B71, 12.15-14.00? | Lp-spaces. Normed spaces. (Sections 1.3 and 2.1.)? | Lp-spaces. H?lder's and Minkowski's inequalities. Examples of normed spaces.? |
| 01.09.2008 | NL? | B62, 12.15-14? | Normed spaces (Sections 2.1 and 2.2)? | The spaces L\infty and l\infty. Finite-dimensional normed spaces. Equivalent norms.? |
| 02.09.2008 | NL? | B71, 12.15-14? | Banach spaces (Section 2.2)? | ? |
| 08.09.2008 | NL? | B62? | Exercises, section 2? | Exercises for week 37.? |
| 09.09.2008 | NL? | B 62? | Hilbert spaces (Section 3.1)? | ? |
| 15.09.2008 | NL? | B62, 12.15-14? | Orthogonality. Orthogonal complements.? | Sections 3.2-3.3.? |
| 16.09.2008 | NL? | B71, 12.15-14? | Orthonormal bases in Hilbert spaces? | Section 3.4? |
| 22.09.2008 | NL? | B62? | Exercises. Fourier series? | Exercises for week 39. Solution to the additional exercise for week 37 can be found her.Section 3.5? |
| 23.09.2008 | NL? | B71? | Continuous linear transformations? | Section 4.1? |
| 29.09.2008 | NL? | B62? | Exercises. The norm of a bounded linear transformation? | Exercises for week 40.Section 4.2.? |
| 30.09.2008 | NL? | B71? | The space B(X, Y). Inverses of operators.? | Sections 4.3-4.4 (Theorem 4.43, Corollary 4.44, Theorem 4.52 will be stated without proofs.)? |
| 06.10.2008 | NL? | B62? | Exercises. Inverses of operators. Dual spaces.? | Exercises for week 41.Finish section 4.4.Section 5.1.? |
| 07.10.2008 | NL? | B71? | Seminorms. The second dual. Dual operators.? | Section 5.2 (sublinear functionals and seminorms.)Section 5.3 (The Hahn-Banach extension theorem in normed spaces, Thm. 5.19, will be stated without proof.) Section 5.5. ? |
| 13.10.2008 | NL? | B62? | Exercises. The adjoint of an operator on Hilbert space.? | Exercises for week 42: 5.2, 5.15, example 5.40.Section 6.1.? |
| 14.10.2008 | NL? | B71? | Normal, self-adjoint and unitary operators on Hilbert spaces? | Section 6.2.? |
| 20.10.2008 | NL? | B62? | Exercises. The spectrum of an operator? | Exercises for week 43.Section 6.3? |
| 21.10.2008 | NL? | B71? | The spectrum of an operator. Positive operators. Projections.? | Sections 6.3 - 6.4.? |
| 27.10.2008 | NL? | B62? | Exercises. Compact operators.? | Exercises for week 44.Section 7.1? |
| 28.10.2008 | NL? | B71? | Compact operators. Spectral theory.? | Sections 7.1-7.2.? |
| 03.11.2008 | NL? | B62? | Exercises. Spectral theory of compact operators.? | Exercises for week 45: 7.2, 7.3, 7.8, 7.11.? |
| 04.11.2008 | NL? | B71? | Spectral theory of compact operators. The Fredholm alternative.? | Section 7.2.? |
| 10.11.2008 | NL? | B62? | Self-adjoint compact operators.? | Section 7.3.? |
| 11.11.2008 | NL? | B71? | Self-adjoint compact operators.? | Section 7.3.? |
| 17.11.2008 | NL? | B62? | Fredholm integral equations.? | Section 8.1.? |
| 18.11.2008 | NL? | B71? | Volterra operators.Applications to solving differential equations.? | Section 8.2. Section 8.3 (up to Thm. 8.18).? |
Teaching plan
Published Aug. 25, 2008 4:51 PM
- Last modified Oct. 28, 2008 10:47 AM