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Functional Analysis


  • The results of the resit are now uploaded and accessible via TUM-Online!, LMU students can get there results here.
  • The results are now uploaded and accessible via TUM-Online!, LMU students can get there results here.
  • Here is a list of exercises from the problem sheets that are at the level of the examination.
  • Here is a list with the matriculation numbers of all LMU students that have successfully registered for the examination.
  • There is no lecture on Friday 23.12.2016 due to closeness to Christmas.
  • There is no exercise class on Wednesday 7.12.2016 due to "Dies Academicus".
  • We cannot accept further registrations of LMU students for the examination! All students that registered before end of October are still welcome to participate in the examination. All others we refer to the lecture at LMU next summer term. For further details please contact the director of studies (Studiendekan) of LMU.
  • The exercise session on Thursday, 10.11.2016 will be preponed to 10:15 am in room 00.13.054.
  • Exercise Sessions will start in the second week.
  • Lecture on Friday, 3.2.2017, takes place in Physik Hörsaal 2 (Room 2502)


  • Examination
    • first attempt: 03.03.2017, 4-5:30 PM, MW 2001, Rudolf-Diesel-Hörsaal
    • resit: 19.04.2017, 11 AM - 12:30 PM, MW 1801, Ernst-Schmidt-Hörsaal
    • you can bring 1 DIN A4 sheet of paper (= 2 pages) handwritten notes
    • Here is a list with the matriculation numbers of all LMU students that have successfully registered for the examination. TUM students register via TUMonline.
    • Exercises will be formulated in German and English. The solution can be written in one of these languages.
    • Please bring your student ID and a valid Personalausweis or Passport to the examination.

  • Lectures
    • Lecturer: Dr. Frank Filbir Pfeil
    • Module Number: MA 3001
    • ECTS-Points: 9
    • Time: Tue 2-4 PM, Fr 2-4 PM
    • Place: Tue: 2502 (Physik Hörsaal 2), Fr: 2501 (Rudolf-Moßbauer-Hörsaal)

  • Exercise Session
    • Organization: Dr. Sara Krause-Solberg
    • Group 1: Mo 4:15-5:45 PM, Room 03.10.011, Sara Krause-Solberg
    • Group 2: Tue 8:15-9:45 AM, Room 03.10.011, Sarah Rathbauer/Sara Krause-Solberg
    • Group 4: Th 2-3:30 PM, Room 03.08.011, Rufat Badal
    • Group 5: Wed 5-6:30 PM, Room 03.06.011, Rufat Badal


Additional material

Problem Sets

We strongly encourage you to solve the problems on the exercise sheets before attending the problem session. Ask whenever you couldn’t solve a problem. There will be no written corrections of the homework, so present your solution at the board to get feedback.

Sheet 1 for exercise classes on 24.-27. October 2016
Sheet 2 for exercise classes on 31. October - 03. November 2016
Sheet 3 for exercise classes on 07.-10. November 2016
Sheet 4 for exercise classes on 14.-17. November 2016
Sheet 5 for exercise classes on 21.-24. November 2016
Sheet 6 for exercise classes on 28. November - 1. Dezember 2016
Sheet 7 for exercise classes on 5.-8. Dezember 2016
Sheet 8 for exercise classes on 12.-15. Dezember 2016
Sheet 9 for exercise classes on 19.-22. Dezember 2016
Sheet 10 for exercise classes on 09.-12. January 2017
Sheet 11 for exercise classes on 16.-19. January 2017
Sheet 12 for exercise classes on 23.-26. January 2017
Sheet 13 for exercise classes on 30. January - 2nd February 2017
Sheet 14 for exercise classes on 6.-9. February 2017

Selected solutions

Here are the drafts of the solutions we did not cover in the exercise classes (Thank you, Rufat).
Solution of 2.3
Solutions Sheet 3
drafts, additional information Pfeil, added on February 17th.


* N. Bourbaki, General Topology: Chapters 1-4, Springer Science & Business Media, 1998.
* G. Preuß, Allgemeine Topologie, Springer-Verlag, 2013. (German)
* J. Dugundji, Topology, Allyn and Bacon, 1966.

Functional Analysis
* J. B. Conway, A Course in Functional Analysis, Springer, 1990
* K. Yoshida, Functional Analysis, Springer, 1995
* D. Werner, Funktionalanalysis, Springer, 2011
* E. Hille, R.S. Phillips, Functional Analysis and Semi-Groups, AMS Colloquium Publications, Vol. 31, 1957
* P. Lax, Functional Analysis, Wiley, 2002
* G. Köthe, Topologische lineare Räume I., Springer, 1966
* W. Rudin, Functional Analysis, Mc Graw-Hill, 1991
* F. Treves, Topological Vector Spaces, Academic Press, 1967
* M. Reed, B. Simon, Methods of Modern Mathematical Physics I: Functional Analysis, Academic Press, 1980
* R. Larsen, Functional analysis: an introduction, Vol. 15 of Monogr. and textb. in pure and appl. math., Dekker, 1973
* A. Robertson, W. Robertson, Topological Vector Spaces, Vol. 53 of Cambridge Tracts in Math., CUP Archive, 1980