Functional Analysis II Spring 2023

Peter Hintz
Pieter-Bart Peters
Teaching Assistants
Valentin Bosshard, Hjalti Isleifsson


Unbounded operators, self-adjoint operators, continuous, Borel functional calculus, spectral theorem for bounded operators, spectral theorems for unbounded operators, elliptic partial differential equations, Sobolev spaces on an interval, Sobolev spaces in higher dimensions, Sobolev embedding theorems, Rellich compactness, trace theorem, Sobolev regularity of weak solutions, Weyl's law, wave equation and scattering theory.


This is the follow-up course of the Functional Analysis I, taught in HS2022. Familiarity with the following concepts is assumed: Baire category theorem; Banach and Hilbert spaces, bounded linear operators; basic principles: uniform boundedness, open mapping/closed graph theorem, Hahn-Banach theorem; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu theorem; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces.

Lecture Summaries And Additional Documentation

Below will follow a diary of the lectures. The recordings of the lectures can be found here. !!!Achtung!!! The final lecture was recorded via zoom here. Handwritten notes of the lectures and additional documentation can be found here. Lecture notes of the FA I course can be found here. Furthermore, Hjalti has been kind enough to create write-ups of his exercise classes here, containing useful extra examples of concepts discussed during the lectures.

Office hours

During the lecture-free period, Pieter-Bart will hold weekly office hours each Monday over zoom, from 09:00-10:30, starting from 19.06.2023. Here you can ask any questions regarding the lectures, the exercises or the exam. Sending questions in advance is recommended. The zoom link is here and can be accessed with the password you received in your e-mail.


The new exercises will be posted on Fridays. They will be discussed in class the following Monday and can be handed in a week later on Monday (10 days after original publication).

exercise sheet due by solutions
Exercise sheet 1 March 6 Solutions 1
Exercise sheet 2 March 13 Solutions 2
Exercise sheet 3 March 20 Solutions 3
Exercise sheet 4 March 27 Solutions 4
Exercise sheet 5 April 3 Solutions 5
Exercise sheet 6 April 17 Solutions 6
Exercise sheet 7 April 24 Solutions 7
Exercise sheet 8 May 1 Solutions 8
Exercise sheet 9 May 15 Solutions 9
Exercise sheet 10 May 22 Solutions 10
Exercise sheet 11 May 29 Solutions 11
Exercise sheet 12 June 6 Solutions 12


Exercises can be handed in with SAM-UP here.

Exercise classes

Mo 09-10HG E 33.3Valentin Bosshard
Mo 09-10HG F 26.5Hjalti Isleifsson