Lecturer

Prof. Dr. Marc Burger

Coordinator

Beat Zurbuchen

Lectures

Monday, 10 - 12, CAB G 51
Thursday, 14 - 16, CAB G 61

Content

This course is the continuation of Functional Analysis I and teaches more advanced topics in functional analysis. It encompasses a variety of subjects such as Banach Algebras, the Gelfand Duality theorem, spectral theorems, and harmonic analysis on LCA groups. It culminates with a proof of the Pontryagin duality theorem and Wiener's theorem.

We have a forum! If you have any questions on the materials, the exercises and/or the solutions, please make a post here.

You can find the script for the course here.

Here you can find additional notes to the course:

• Ultrafilters and the Guelfand spectrum of \(\ell^\infty(\mathbb{N})\)
• Spectral theorem for a normal operator

Exercises

The new exercises are posted here on Thursdays. We hope that you look at the problems over the weekend and prepare some questions for the exercise class on Monday.

Please hand in your solutions on the second Monday until midnight after on the SAMup. This will guarantee that your assistant corrects your submission.

Some of the exercises are marked with a *. These exercises are not part of the curriculum and are meant as a challenge.

Exercise classes

The exercise classes take place on Monday from 9 - 10. Please register for one of the exercise classes in MyStudies at the beginning of the semester. Please note that the exercise classes start only from the second week of the semester.

Literature

• M. Einsiedler and T. Ward. Functional analysis, spectral theory, and applications. Vol. 276. Graduate Texts in Mathematics. Springer, 2017.
• I. Gelfand, D. Raikov, and G. Shilov. Commutative normed rings. Translated from the Russian, with a supplementary chapter. Chelsea Publishing Co., New York,1964.
• E. Kaniuth. A Course in Commutative Banach Algebras. Vol. 246. Graduate Texts in Mathematics. Springer, New York, 2009.
• D. Ramakrishnan and R. J. Valenza. Fourier Analysis on Number Fields. Vol. 186. Graduate Texts in Mathematics. Springer, New York, 1999.
• W. Rudin. Fourier Analysis on Groups. Interscience Tracts in Pure and Applied Mathematics 12. Interscience Publishers, New York-London, 1962.
• W. Rudin. Functional Analysis. Second Edition. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, 1991.
• W. Rudin. Real and Complex Analysis. Third Edition. McGraw-Hill Book Co., New York, 1987.
• M. Takesaki. Theory of Operator Algebras I. Springer, New York, 1979.
• A. Weil. Basic Number Theory. Classics in Mathematics. Reprint of the second (1973) edition. Springer Berlin, Heidelberg, 1995.
• R. J. Zimmer. Essential Results of Functional Analysis. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1990.