What is the Topic of this Course?

Dear Participants,

the moment of truth has arrived: Lecture 1 is uploaded to the wiki page, and you can download it by clicking on the PDF link below.

In this lecture, we set the stage for the course with the aim to motivate why operator semigroups, the central objects of our study, are important. We have deliberately chosen examples that might be known to you so that our point gets through.

It is customary to mention in every lecture and book on operator semigroups the famous quote by Einar Hille, one of the founding fathers of this theory:

"I hail a semigroup when I see one and I seem to see them everywhere!"

We now break this tradition and do not quote Hille in the lectures, but the course will be full of semigroups.

For us, the word "semigroup" means a one-parameter semigroup of operators, which, being a synonym for a (semi-) dynamical system, occurs in numerous applications. The semigroup property reflects the deterministic time-evolution of a system, and we shall see a great number of examples of time-dependent partial differential equations which can be treated in the framework of semigroup theory. More on this idea will follow in the lectures.

All of you are most welcome to comment the lectures and the exercises in the relevant discussion pages, and everyone is encouraged to solve the exercises.

To make sure that every one of them gets solved, each week we shall assign a team to produce an "official" PDF version of the solutions. For the first week we ask the team of Budapest to do this. Please send us your solutions as an attachment to an e-mail and we shall make the files available on the wiki.

Enjoy reading,
your virtual lecturers,

Alexander
András
Bálint
Petra

ISEM15_Lecture1-v02.pdf -- corrected version --

Discussion of Lecture 1.

Solutions and discussion of the exercises.