Course: Functional Analysis II (WS2019/2020)
An important result of linear algebra is that every self-adjoint linear map on a finite-dimensional inner-product space can be represented by a diagonal matrix. In this course we will study the spectral theorem, which generalises this result to self-adjoint operators on infinite-dimensional Hilbert spaces, including to unbounded operators. We will also acquire the necessary tools to use this result in applications, for example to partial differential equations and quantum mechanics. These include the Fourier transform, the theory of self-adjoint extensions, and quadratic forms.
Lectures: Wednesdays 08:30-10:00 Room B 039 and Thursdays 10h-12h Room B 132.
Examination: To pass the course you will need to take the final exam.
The Exam will take place on the 06.02.2020 from 10:00 to 13:15 in B 132. You may use your personal notes, the lecture notes,
and texbooks in the exam.
You can improve your grade through the homework sheets (more than 50% of total points: +1/3; more than 75%: +2/3)