401-3461-00L Functional Analysis I
Semester | Autumn Semester 2018 |
Lecturers | M. Einsiedler |
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. Einsiedler | ||||||||||||
401-3461-00 U | Functional Analysis I | 1 hrs |
| M. Einsiedler |
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; Fourier transform and applications. |
Learning 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 book Functional Analysis, Spectral Theory, and Applications by Manfred Einsiedler and Thomas Ward and available by SpringerLink. Other useful, and recommended references include the following: Lecture Notes on "Funktionalanalysis I" by Michael Struwe Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011. Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002. Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991. |
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) | |
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ECTS credits | 10 credits |
Examiners | M. Einsiedler |
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 |
Additional information on mode of examination | The active participation in the exercise class via presentations as a voluntary learning task will be graded and can improve the total course unit grade by up to 0.25 grade points. Students can still achieve the maximum grade of 6 in the course unit even if they only sit the final examination. |
Written aids | None |
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 | Book for course |
Only public learning materials are listed. |
Groups
No information on groups available. |
Restrictions
There are no additional restrictions for the registration. |