Department Mathematik



Exercises in
Functional Analysis, summer 2015

This site provides informations and materials on the exercise and tutorial sessions
complementing the lecture course Functional Analysis held by

Prof. Martin Fraas, PhD.
Office: Room B 329
Office hours: Tuesday 10:30 - 12:00 and 14:00 - 17:00, or by appointment.


10.11.2015 This site will no longer be updated.
21.10.2015 The results of the make-up exam can be found near the old office of Prof. Martin Fraas (B 329). You can review your exam on Wed, Nov 4 2015, from 13:30 to 13:45 in B 410.
25.09.2015 The registration for the make-up exam is closed. Please read the updated information (all participants will be in B 052).
21.08.2015 The registration for the make-up exam is enabled.
04.08.2015 An updated list of the results of the exam can be found near the office of Prof. Martin Fraas.
29.07.2015 You can review your exam on Thursday, July 30th, at 13:30 in room B 101.
29.07.2015 See here for more details regarding the make-up exam.
27.07.2015 If you need a certificate (Schein), please get in touch with Prof. Martin Fraas as soon as possible!
23.07.2015 Tomorrow, Friday July 24th, at about 16:00, we will pin a list with the results of the exam near the office of Prof. Fraas. You can review your exam on Thursday, July 30th, at 13:30 (room B 101).
15.07.2015 See here for more details regarding the exam.
30.06.2015 A typo in Exercise 5 on Sheet 11 has been corrected (definition of a symmetric operator).
15.06.2015 We added the assumption that the Hilbert space in Exercise 1 on Sheet 9 is separable.
09.06.2015 The formulation of Exercise 4 on Sheet 8 was updated.
26.05.2015 A draft of the solution to sheet 5 can be found here.
24.05.2015 The assignment discussion on Tuesday, May 26th, will not take place. Instead there will be a draft of the solutions available for download. In order to make up for the Tutorial sessions on Monday and Tuesday, feel free to attend any of the remaining Tutorial classes.
04.05.2015 Since there are no lectures on Tuesday, May 26th, we changed the date for the final hand in of the third and the first hand in of the fifth exercise sheet to Friday, May 22nd at 12:15.
28.04.2015 In order to keep it as simple as possible, we ask you to always hand in your solution at the final hand in again, even if your first solution was correct. Note also that according to the rules you can only get credit for those exercises you tried to solve in the first round. Thus, in the final hand in you need to attach your first solution as well.
20.04.2015 A remark has been added to Exercise 2 on Sheet 1 (Do not worry about making a rigorous computation. This exercise is supposed to be solved in the style of the 19th century.)
11.04.2015 The first lecture starts on Tuesday April 14, the tutorial classes start on Monday April 20, while the first assignment discussion (Zentralübung) will be on Tuesday April 28.

General Informations

Please read FAInfo.pdf for a detailed description of the rules, the exercise schedule, and the bonus system.

Lecture Notes

The official lecture notes can be found here.

Notes typeset by T. Simonis can be found here. The notes were not officially proof checked.


The registration for the lecture is closed.

In the process of registration for the tutorial classes you may choose one out of five dates (see the timetable below). Take your time in choosing the correct group, since you won't be able to change it afterwards by yourself. If you just want to do the weekly homework assignments without participating in the tutorial sessions, then please choose group X. This will help keeping the number of registered students that never attend classes at a minimum, while freeing up the slots for those who really want to come.

The data submitted during the process of registration will be kept private and won't be published at any time.


Monday Tuesday Wednesday Thursday Friday
Prof. M. Fraas
B 051
Tutorial B
Adrian Dietlein
B 134
Tutorial E
Bernhard Pfirsch
B 134
Prof. M. Fraas
C 123
Tutorial A
Andreas Groh
B 133
Tutorial C
Simon Bürger
B 041
Tutorial D
Tobias König
B 251
Assignment Discussion
Sebastian Gottwald
B 139
Remark. Even though the lecture is held in English, you are free to speak German in your tutorial class. Tutorial A will be in English if necessary.


1st hand in
1st return
Final hand in
Mon, Apr 20
Mon, Apr 27, 13:30
Thu, Apr 30
Mon, May 11, 13:30
Mon, Apr 27
Mon, May 4, 13:30
Fri, May 8
Mon, May 18, 13:30
Mon, May 4
Mon, May 11, 13:30
Fri, May 15
Fri, May 22, 12:15
Mon, May 11
Mon, May 18, 13:30
Fri, May 22
Mon, June 1, 13:30
Mon, May 18
Fri, May 22, 12:15
Fri, May 29
Mon, June 8, 13:30
Tue, May 26
Mon, June 1, 13:30
Fri, June 5
Mon, June 15, 13:30
Mon, June 1
Mon, June 08, 13:30
Fri, June 12
Mon, June 22, 13:30
Mon, June 8
Mon, June 15, 13:30
Fri, June 19
Mon, June 29, 13:30
Mon, June 15
Mon, June 22, 13:30
Fri, June 26
Mon, July 6, 13:30
Mon, June 22
Mon, June 29, 13:30
Fri, July 3
Mon, July 13, 13:30
Mon, June 29
Mon, July 6, 13:30
Fri, July 10
Wed, July 15, 12:00
Mon, July 6


The final exam took place on July 22nd, 2015, between 9:00 and 12:00 (150 min).

Make-up Exam

The make-up exam took place on Sept 28th, 2015, between 9:00 and 12:00 (150 min).


Lecturer. The lectures are held by Prof. Martin Fraas, PhD.

Assistants. The exercise and tutorial sessions are organized by Andreas Groh and Sebastian Gottwald. You can find our office hours on our websites.

Tutors/Markers. Don't hesitate to ask questions during the tutorial sessions even though they are not directly related to the current exercise sheet. If you want to contact your tutor during the week, you can find his mail address below.

Token Marker E-Mail
AD Adrian Dietlein
AN Alex Niederklapfer
BP Bernhard Pfirsch
SB Simon Bürger
TK Tobias König