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Workgroup Applied Analysis

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 2.029

Address
Englerstrasse 2
76131 Karlsruhe
Germany

Dr. Kaori Nagato-Plum
kaori.nagatou@kit.edu




Office hours:
Mon - Fri 10:00 -- 12:00

Tel.: +49 721 608 42056

Fax.: +49 721 608 46214

Functional Analysis (Winter Semester 2010/11)

Lecturer: Dr. Agnes Radl
Classes: Lecture (1048), Problem class (1049)
Weekly hours: 4+2


Exam Results

The results of the examination are published next to room 3A-17 in the Allianz building.



Lecture Notes

Version 1 (2011-02-17)

The password to open the file was given in the lecture. If you forgot the password feel free to contact me.

Schedule
Lecture: Tuesday 9:45-11:15 Nusselt-Hörsaal
Thursday 11:30-13:00 Hertz-Hörsaal
Problem class: Friday 14:00-15:30 Eiermann
Lecturers
Lecturer Dr. Agnes Radl
Office hours:
Room Allianz-Gebäude (05.20)
Email: agra@fa.uni-tuebingen.de

The lecture covers fundamental aspects of linear functional analysis.

Topics:

  • metric spaces, Banach spaces, bounded linear operators
  • main principles of functional analysis (Hahn-Banach theorem, principle of uniform boundedness, closed graph theorem)
  • weak convergence, Banach-Alaoglu theorem
  • Hilbert spaces
  • Fourier transform


Exercise sheets

Exercise sheet 1
Exercise sheet 2
Exercise sheet 3
Exercise sheet 4
Exercise sheet 5
Exercise sheet 6
Exercise sheet 7
Exercise sheet 8
Exercise sheet 9
Exercise sheet 10
Exercise sheet 11
Exercise sheet 12
Exercise sheet 13
Exercise sheet 14

References

  • H.W. Alt: Lineare Funktionalanalysis, Springer 2002.
  • J.B. Conway: A Course in Functional Analysis, Springer 1990.
  • H. Heuser: Funktionalanalysis, Teubner 2006.
  • S. Lang: Real and Functional Analysis, Springer 1993.
  • P.D. Lax: Functional Analysis, Wiley 2002.
  • M. Reed, B. Simon: Methods of Modern Mathematical Physics: Functional analysis, Academic Press 1980.
  • W. Rudin: Functional Analysis, McGraw-Hill 1991.
  • B.P. Rynne, M.A. Youngson: Linear Functional Analysis, Springer 2008.
  • M. Schechter: Principles of Functional Analysis, Academic Press 1973.
  • S. Shirali, H.L. Vasudeva: Metric Spaces, Springer 2006.
  • A.E. Taylor, D.C. Lay: Introduction to functional analysis, Wiley 1980.
  • D. Werner: Funktionalanalysis, Springer 2007.