Fundamentals of One-Parameter Semigroups

Dear Participants,

we are pleased to see the interest in our lectures and thank you for all the comments and contributions on the discussion pages.

Lecture 2 has been uploaded to the wiki page, but please, do not hesitate to continue making remarks also on Lecture 1.

As we have seen in the previous lecture, operator semigroups play a central role in this course. They generalise the exponential function and allow the rigorous treatment of time discretisation methods. Semigroup theory provides also a powerful framework to space discretisation methods like finite elements. However, to get to these applications, we have to show basic properties of semigroups.

In this lecture we give an overview of the basic properties of semigroups. You will learn the consequences of strong continuity, how to define the infinitesimal generator, and what its most fundamental properties are. The results might seem abstract at the first sight, but we ask you to trust us: these technicalities will be needed later on.

The lecture can be downloaded by clicking on the PDF link below.

We kindly ask the team at Darmstadt to provide the "official" solutions.

Best wishes and good reading,
your ISEM-Team
Alexander
András
Bálint
Petra

ISEM15_Lecture2.pdf

A corrected version will be uploaded soon, until then see:

Discussion of Lecture 2.

Solutions and discussion of the exercises.