Inhalt:

Die Funktionalanalysis ist der Zweig der Mathematik, der sich mit der Untersuchung von normierten (oder allgemeiner topologischen) Vektorräumen und stetigen Abbildungen zwischen ihnen befasst. Hierbei werden Analysis, Topologie und Algebra verknüpft. Die Vorlesung behandelt Banach- und Hilberträume, lineare Operatoren und Funktionale sowie Spektraltheorie kompakter Operatoren.

Organization

Lecture:  Wed & Thu 8:30am - 10:00am
Exercise: Thu 2:15pm - 3:45pm

Team

Lectures:

• Maximilian Engel (maximilian.engel@fu-berlin.de)
• Péter Koltai (peter.koltai@fu-berlin.de)

Exercises:

• Patrick Gelß (p.gelss@fu-berlin.de)
• Mattes Mollenhauer (mattes.mollenhauer@fu-berlin.de)

Lecture

The lectures will be held online in Webex Meetings. The link to the events will be communicated through the Announcements. Please join with your video turned on and feel free to ask question just like in class with physical presence.
Lecture notes and additional material will be provided in Resources.

Exercise class

Tutorial sessions will be held online via Webex, just like the main lecture.

The link to the exercise sessions can be found in the announcements.

There will be exercise sheets. It is expected that you prepare presentations of solutions to the exercises - you will not be required to submit written solutions. However, for the active participation ("aktive Teilnahme") you will be required to present at least two solutions, at least one in each half of the semester.

Possible ways to participate in the tutorial sessions are sharing your screen and presenting a particular exercise via

• short and concise LaTeXed notes; or
• a readable scan/photo of a handwritten document; or
• deriving a solution live on a note taking app (Microsoft OneNote, Samsung Notes etc.) if you have access to a tablet (preferred); or
• additional ideas are always welcome.

Before presenting in a tutorial session, please perform a screen share in a test session with the Webex application on your platform. 

Exams

The exam (Klausur) will take place on Wed, February 23, 2022, from 8:00am to 09:30am in the lecture hall of Arnimallee 3 (A3 Hörsaal).

The repeat exam (Nachklausur) will take place on Wed, April 13, 2022, from 8:00am to 09:30am in the seminar room 031 in the Arnimallee 6 (A6 / SR031).

Prerequisites 

• Calculus (Analysis I-II)
• Linear algebra (Lineare Algebra I-II)

Literature

• [Con] J. B. Conway, A course in functional analysis, 2nd edition, Springer, 1990.
• [Kre] E. Kreyszig. Introductory Functional Analysis with Applications. Wiley, 1978.
• [Rud] W. Rudin, Functional Analysis, McGraw-Hill, 1991.
• [Wer] D. Werner, Funktionalanalysis, 7. Aufl., Springer, 2011.
• [Zei] E. Zeidler, Applied Functional Analysis. Main Principles and Their Applications. Springer, 1995