Sobolev spaces, weak solutions of elliptic boundary value problems, elliptic regularity, spectral theory, and unitary representations.
Objective
Acquiring the language and methods for boundary value problems, Sobolev spaces, Banach algebras, Spectral theory of bounded and unbounded selfadjoint operators, and Unitary representations.
Lecture notes
Functional Analysis, Spectral Theory and Applications. Manfred Einsiedler and Thomas Ward, GTM Springer 2017
Literature
Functional Analysis, Spectral Theory and Applications. Manfred Einsiedler and Thomas Ward, GTM Springer 2017
Prerequisites / Notice
Functional Analysis I plus a 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)
The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examination
oral 30 minutes
Additional information on mode of examination
30 minutes preparation and 30 minutes exam (one candidate prepares during the 30 minutes oral exam of the previous candidate).
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.
This information can be updated until the beginning of the semester; information on the examination timetable is binding.