406-3461-AAL  Functional Analysis I

SemesterAutumn Semester 2018
LecturersM. Einsiedler
Periodicityevery semester recurring course
Language of instructionEnglish
CommentEnrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.


406-3461-AA RFunctional Analysis I
Self-study course. No presence required.
300s hrsM. Einsiedler

Catalogue data

AbstractBaire 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.
ObjectiveAcquire 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.
LiteratureWe 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.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits10 credits
ExaminersM. Einsiedler
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationwritten 180 minutes
Additional information on mode of examinationStudents are allowed to participate in the exercise class for the course unit 401-3461-00L and transfer the bonus *) to the course unit 406-3461-AAL.
*) 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 aidsNone
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

Recordinglecture homepage
LiteratureBook for Course
Only public learning materials are listed.


No information on groups available.


There are no additional restrictions for the registration.

Offered in

Mathematics MasterCourse Units for Additional Admission RequirementsE-Information