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 2:15pm - 3:50pm (A3/SR 120)
Exercise: Thu 4:15pm - 5:45pm (A6/SR 009)

Team

Lectures:

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

Exercises:

• Dennis Chemnitz
• Robin Chemnitz

Lectures

Lectures notes will be uploaded under Resources a couple of days prior to the lectures. It is strongly recommended that you consult these notes ahead of the lectures.

Exercise class

There will be exercise sheets, to be found under Resources around Thursday every week. 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.

Exams

The exam (Klausur) is going to take place on Thursday, 23.02.2023, between 2pm - 4pm in A6 SR025/026 (Last name A-M) and SR032 (Last name N-Z).

The retake exam (Nachholklausur) is going to take place on Wednesday 05.04.2023, between 10am - 12am in A6 SR025/026.

Auxiliaries: You will be allowed to bring a handwritten sheet (double-sided).

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