Difference between revisions of "NMMO302 Functional analysis for physicists"
From Josef Málek
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Link to SIS [https://is.cuni.cz/studium/eng/predmety/index.php?id=061695605b45da5bb3803e7550e4e8b2&tid=&do=predmet&kod=NMMO302&skr=2021&fak=11320] | Link to SIS [https://is.cuni.cz/studium/eng/predmety/index.php?id=061695605b45da5bb3803e7550e4e8b2&tid=&do=predmet&kod=NMMO302&skr=2021&fak=11320] | ||
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| + | == Syllabus and exams == | ||
| + | |||
| + | [[Media:NMMO302.pdf|Syllabus, general comments to the exam, literature]] SS 2021/2022 <!-- [[Media:NMMO302.pdf]] --> | ||
| + | |||
| + | [[Media:NMMO302Zk-1.pdf|Sample exam]] <!-- [[Media:NMMO302Zk.pdf]] --> | ||
== Lectures == | == Lectures == | ||
| − | [[Media:LFA_1v1.pdf|Introduction.]] | + | [[Media:LFA_1v1.pdf|1. Introduction.]] |
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| + | [[Media:LFA_2v1.pdf|2. Linear operators between Banach spaces; boundedness, examples and finite-dimensional vector spaces.]] | ||
| − | [[Media: | + | [[Media:LFA_3v2.pdf|3. Seminorms and Frechet spaces. Hahn-Banach theorem.]] |
| − | [[Media: | + | [[Media:LFA_4v2.pdf|4. Dual spaces. Reflexivity. Weak and weak-star convergences.]] |
| − | [[Media: | + | [[Media:LFA_5v1.pdf|B. Baire's theorem.]] |
| − | [[Media: | + | [[Media:LFA_6v2.pdf|5. Great theorems of LFA.]] |
| − | [[Media: | + | [[Media:LFA_7v1.pdf|6. Adjoint operators. Compact operators.]] |
| − | [[Media: | + | [[Media:LFA_8v2.pdf|7. Linear operators in Hilbert spaces. Riesz representation theorem.]] |
| + | |||
| + | [[Media:LFA_9v2.pdf|8. Fredholm theory/Fredholm alternative.]] | ||
| + | |||
| + | [[Media:LFA_10v1.pdf|9. Spectrum. An introduction to spectrum theory.]] [[Media:LFA_10bv1.pdf|9. Spectrum focusing on Hilbert spaces over complex scalars.]] | ||
| + | |||
| + | [[Media:LFA_AAv2.pdf|A. Arzela-Ascoli theorem. (in czech)]] | ||
| + | |||
| + | [[Media:LFA_Cv1.pdf|C. Bases in vector spaces.]] | ||
| + | |||
| + | [[Media:LFA_Fv1.pdf|F. Abstract Fourier series. (in czech)]] | ||
== Recordings == | == Recordings == | ||
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Week 12 - [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_29.mp4 L30] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_31.mp4 L30] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_32.mp4 L31] | Week 12 - [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_29.mp4 L30] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_31.mp4 L30] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_32.mp4 L31] | ||
| + | |||
| + | Week 13 - [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_33.mp4 L33] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_34.mp4 L34] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_35.mp4 L35] | ||
== Problems == | == Problems == | ||
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== Homeworks == | == Homeworks == | ||
Latest revision as of 16:41, 20 May 2022
Link to SIS[edit]
Link to SIS [1]
Syllabus and exams[edit]
Syllabus, general comments to the exam, literature SS 2021/2022
Lectures[edit]
3. Seminorms and Frechet spaces. Hahn-Banach theorem.
4. Dual spaces. Reflexivity. Weak and weak-star convergences.
6. Adjoint operators. Compact operators.
7. Linear operators in Hilbert spaces. Riesz representation theorem.
8. Fredholm theory/Fredholm alternative.
9. Spectrum. An introduction to spectrum theory. 9. Spectrum focusing on Hilbert spaces over complex scalars.
A. Arzela-Ascoli theorem. (in czech)
F. Abstract Fourier series. (in czech)
Recordings[edit]
Week 9 - L22
