Lecturer

Peter Hintz

Coordinator

Pieter-Bart Peters

Teaching Assistants

Valentin Bosshard, Hjalti Isleifsson

Content

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.

Prerequisites

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.

Exercises

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).

SAMup

Exercises can be handed in with SAM-UP here.

Exercise classes

Literature

• Functional Analysis I&II, by M. Struwe (2020 lecture notes).
• Functional Analysis, Volume I by M. Reed and B. Simon (Methods of Modern Mathematical Physics 1983)
• Elliptic Partial Differential Equations of Second Order by D. Gilbarg and N.S. Trudinger (Springer-Verlag 2001 reprint)