PhD Course 2009

An Introduction to Pseudospectra and their Applications

Lecture 1

The program for the first day is as follows:

12:30-12:45

Introduction. Presentations of participants. Formalities regarding the course.

12:45-13:45

A slide presentation of the main points of the course. This presentation will be quite rapid, and you should think of it as a preview of things to come. Some of the items on the slides will take several hours to explain properly. The slides can be found here.

13:45-14:05

Coffee break.

14:05-14:55

Lecture on linear algebra. I will review a number of well known results, and present a number of new concepts. The material covered corresponds roughly to pages 2-6 in the lecture notes.

14:55-15:05

Break.

15:05-16:00

Lecture on operator theory. I will present a number of results, which are valid in both finite dimensional and the infinite dimensional case. A the end I will get to the formal definition of the pseudospectra. I will cover most of the material on pages 11-17 in the lecture notes.

Exercises

I recommend doing the exercises in the lecture notes, as we progress through the material. As of tomorrow I will include time for discussion of the exercises in the schedule.

In connection with the material presented today I recommend looking at the following exercises:

• Exercise 2.4
• Exercise 2.8
• Exercise 4.2
• Exercise 4.4