ISem23

Dear Participants of ISem 23,

We have just uploaded the fifth lecture, which you can find at the following link

https://www.mat.tuhh.de/veranstaltungen/isem23/_media/lecture_05.pdf

or in the forum.

In this lecture, we provide the spectral representation of the time derivative as multiplication operator. The associated unitary transformation is a shifted variant of the Fourier transformation, the so-called Fourier–Laplace transformation.

This explicit spectral representation will not only provide some more insight in the time derivative, but this representation will serve to define a functional calculus for the time derivative. With this functional calculus we will then introduce another central notion of evolutionary equations: the notion of material laws.

It is great that many of you have already used the forum for discussions. Thank you for that!

We hope to receive many solutions to the exercises again. We particularly ask the team from Ulm to provide solutions to the exercises for us to upload.

With the best regards,

the virtual lecturers