Functional Analysis II - Operator Theory (SS 2023)

Lecture Course Functional Analysis II - Operator Theory (SS 2023)

Prof. Dr. Robert Denk

• Time and place: Tuesday 10.00-11.30 in F 420
• 2 + 1 SWS / 4.5 Credits
• Language: planned in German, but English if required
• Organization of exercise groups and lecture notes in ILIAS

Content: This lecture is a continuation of the lecture course Functional Analysis from SS 2022. It is suited for students in B.Sc./M.Sc. Mathematics, but also interesting for students of Physics. In the second part of this course, we discuss abstract principles of Functional Analysis (Theorem of Baire, Theorem of Banach-Steinhaus) as well as the spectral theorem for selfadjoint operators. The spectral theorem allows us to define functions of (unbounded) operators. For instance, exp(tΔ)u₀ defines a solution of the heat equation ∂_tu−Δu=0 (t>0),  u(0)=u₀.

As prerequisites, the students should know the standard lectures from the first three semesters as well as the content of Functional Analysis, Part 1, from SS 2022.

Lecture notes: The lecture notes are written in parallel to the lectures and can be found in ILIAS.

Module exam: For a success in the modul, the students have to participate sucessfully in the exercises (at least 50% of the exercise points and active participation). The exam is planned as an oral exam and can be scheduled individually.