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 == | ||
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| + | [[Media:NMMO302.pdf|Syllabus, general comments to the exam, literature]] SS 2021/2022 <!-- [[Media:NMMO302.pdf]] --> | ||
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== Lectures == | == Lectures == | ||
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[[Media:LFA_9v1.pdf|8. Fredholm theory/Fredholm alternative.]] | [[Media:LFA_9v1.pdf|8. Fredholm theory/Fredholm alternative.]] | ||
| − | [[Media:LFA_10v1.pdf|9. Spectrum. An introduction to spectrum theory.]] | + | [[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_AAv1.pdf|A. Arzela-Ascoli theorem.]] | + | [[Media:LFA_AAv1.pdf|A. Arzela-Ascoli theorem. (in czech)]] |
[[Media:LFA_Cv1.pdf|C. Bases in vector spaces.]] | [[Media:LFA_Cv1.pdf|C. Bases in vector spaces.]] | ||
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| + | [[Media:LFA_Fv1.pdf|F. Abstract Fourier series. (in czech)]] | ||
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== Recordings == | == Recordings == | ||
Revision as of 12:53, 19 May 2022
Link to SIS
Link to SIS [1]
Syllabus
Syllabus, general comments to the exam, literature SS 2021/2022
Lectures
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
Week 9 - L22
Problems
Feb 25: Finite-dimensional vector spaces
