401-3461-00L Functional Analysis I
| Semester | Autumn Semester 2019 |
| Lecturers | M. Struwe |
| Periodicity | yearly recurring course |
| Language of instruction | English |
| Comment | At most one of the three course units (Bachelor Core Courses) 401-3461-00L Functional Analysis I 401-3531-00L Differential Geometry I 401-3601-00L Probability Theory can be recognised for the Master's degree in Mathematics or Applied Mathematics. |
Courses
| Number | Title | Hours | Lecturers | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 401-3461-00 V | Functional Analysis I | 4 hrs |
| M. Struwe | ||||||||||||
| 401-3461-00 U | Functional Analysis I Groups are selected in myStudies. | 1 hrs |
| M. Struwe |
Catalogue data
| Abstract | Baire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces. |
| Objective | Acquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps. |
| Literature | We will be using the Lecture Notes on "Funktionalanalysis I" by Michael Struwe. Other useful, and recommended references include the following books: Haim Brezis: "Functional analysis, Sobolev spaces and partial differential equations". Springer, 2011. Manfred Einsiedler and Thomas Ward: "Functional Analysis, Spectral Theory, and Applications", Graduate Text in Mathematics 276. Springer, 2017. Peter D. Lax: "Functional analysis". Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002. Elias M. Stein and Rami Shakarchi: "Functional analysis" (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011. Walter Rudin: "Functional analysis". International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991. Dirk Werner, "Funktionalanalysis". Springer-Lehrbuch, 8. Auflage. Springer, 2018 |
| Prerequisites / Notice | Solid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces). |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| ECTS credits | 10 credits |
| Examiners | M. Struwe |
| Type | session examination |
| Language of examination | English |
| Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |
| Mode of examination | written 180 minutes |
| Written aids | A short collection of useful results will be provided by the lecturer. |
| This information can be updated until the beginning of the semester; information on the examination timetable is binding. | |
Learning materials
| Main link | lecture homepage |
| Literature | Lecture notes |
| Only public learning materials are listed. | |
Groups
| 401-3461-00 U | Functional Analysis I | ||||||
| Groups | G-01 |
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| G-02 |
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| G-03 |
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| G-04 |
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Restrictions
| There are no additional restrictions for the registration. |
