Lecturer

Josef Teichmann

Coordinator

Christian Beck

Lectures

Mon 10–12 HG D 7.1 Link to live stream of HG D 7.1
Thu 14–16 HG G 5 Link to live stream of HG G 5

Exercise classes

Mon 9–10

First lecture

23.09.2021

Course Catalogue

401-3461-00L Functional Analysis I

Announcements

• Seating plan for the exam on February 2. All students registered for the exam on February 2 obtain their seat number via e-mail.
• Starting Monday, October 4, the exercise class of Valentin Bosshard will be recorded. Please note that it also has been moved to HG G 19.1. Link to livestream of the recorded exercise class
• Starting Monday, October 4, Réné Pfitscher's exercise class takes place in HG G 26.5.

Prerequisites

Solid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with topology and measure theory, in particular Lebesgue integration and \( L^p \) spaces).

Content

Baire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces.

Literature

• Michael Struwe. Funktionalanalysis I und II. Lecture notes, ETH Zürich, 2019/20.
• John B. Conway. A Course in Functional Analysis. Graduate Texts in Mathematics. Springer-Verlag, New York, 2007.
• Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.
• Michael Reed and Barry Simon. Methods of Modern Mathematical Physics – Volume 1 (Functional Analysis). Academic Press, 1981
• Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011.
• Peter D. Lax. Functional analysis. Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], New York, 2002.
• Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.
• Martin Schweizer. Measure and Integration. Lecture notes, ETH Zürich, 2017.

Useful resources

• Terence Tao. Ask yourself dumb questions – and answer them!
• Terence Tao. Think ahead.
• Paul R. Halmos. How to write Mathematics.
• Susan Hermiller, Melanie Martin and Eric York. Learning Calculus.

Exercises

The new exercises will be posted here on Fridays, starting on Friday, September 24. Please hand in your solutions by the following Friday at 12:00. You can do so, e.g., via the upload links below or via your assistant's box in HG F 28. Note, however, that the assistants will only grade up to three exercises per submission. Therefore, please indicate which exercises on your submission you want to have graded.

Exercise classes