Dato | Undervises av | Sted | Tema | Kommentarer / ressurser |
24.08.2010 | Nadia S. Larsen (NSL) | Aud 2, Vilhelm Bjerknes Hus | Presentation of the course. Metric and topological spaces | § 1.1 |
25.08.2010 | NSL | Metric and topological spaces, further properties. | §1.1 | |
31.08.2010 | NSL | The Banach space of continuous functions | §1.2 | |
01.09.2010 | NSL | Banach spaces: definition and examples | §1.2 | |
07.09.2010 | NSL | The geometry of Hilbert spaces. Exercises | §1.3. Problems 1.1, 1.6. | |
08.09.2010 | NSL | Completeness in normed spaces. Bounded operators | § 1.4, § 1.5 | |
14.09.2010 | NSL | Exercises. Sums and quotients of Banach spaces | Problems 1.8, 1.9, 1.10, 1.12 (only for p=2), 1.13, 1.14 | |
15.09.2010 | NSL | Orthonormal bases | § 2.1 | |
21.09.2010 | Sergey Neshveyev | Exercises. The projection lemma and the Riesz lemma. | Problems 1.25 and 1.26. Section §2.2. | |
22.09.2010 | Sergey Neshveyev | Operators defined via forms. Orthogonal sums. Compact operators | Sections §2.3, §2.4 and §3.1. | |
28.09.2010 | NSL | Exercises. Compact operators. | Problems 2.3, 2.4, 2.5, 2.6. Section §3.1. | |
29.09.2010 | NSL | The spectral theorem for compact symmetric operators | §3.2. | |
05.10.2010 | NSL | The spectral theorem for compact symmetric operators. The Sturm-Liouville problem | § 3.2 -3.3. Problem 3.2 and the following problem: let K(x,y)= cos(x-y) and a=0, b=2 pi in Lemma 3.4. Show that z= pi is the only non-zero eigenvalue. Find the corresponding eigenspace. | |
06.10.2010 | NSL | Compact operators. Sturm-Liouville operators. | § 3.3-3.4. | |
07.10.2010 | The obligatory assignment will be posted! | Follow the homepage of the course. | ||
12.10.2010 | NSL | Exercise. Fredholm theory | §3.5. Exercise: use the method of variation of parameters (or variation of constants) to deduce the formula (3.14), in other words use that u+(z,x) and u_(z,x) are solutions for the homogeneous equation to explain why the solution f(x) must be of the form (3.14). | |
13.10.2010 | NSL | Fredholm theory for compact operators | §3.5. | |
19.10.2010 | NSL | Exercises. Borel measures. Premeasures | Problem 3.10. Sections §4.1,4.2 | |
20.10.2010 | NSL | Properties of premeasures and measures | §4.2 | |
26.10.2010 | NSL | Extensions via outer measures. Measurable functions. | §4.2, §4.3. | |
27.10.2010 | NSL | Measurable functions. Integration. | §4.3, §4.4. | |
02.11.2010 | NSL | Integration. The Lebesgue spaces. | § 4.4, §5.1. | |
03.11.2010 | NSL | The Lebesgue spaces. | §5.2 | |
09.11.2010 | NSL | L^p is a Banach space | §5.3. Problems 4.7, 4.8, 5.1. | |
10.11.2010 | NSL | Fourier series in L^2([-\pi, \pi). | Section 1 and the Riemann-Lebesgue lemma in the notes. | |
16.11.2010 | NSL | Types of convergence for Fourier series. Exercises. | Section 2 and exercises 1-3 in the notes.
In addition, problem 4.9. |
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17.11.2010 | NSL | Uniform convergence of Fourier series. Exercises. | Section 4 and exercises 4, 5 in the notes. | |
23.11.2010 | NSL | Product measures. Exercises. | Section 4.5 in Teschl's notes.
Note: this is the last lecture with theory. |
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24.11.2010 | NSL | Exercises | We look at some of the additional exercises. | |
03.12.2010 | NSL | Seminar room 313. Time 10:15-12. | Exercises. | This is an extra session where we go over exercises in this list and this list.
I will also answer questions about the material in the course. |
Undervisningsplan
Published Aug. 18, 2010 4:31 PM
- Last modified Feb. 27, 2023 11:43 AM