PhD Course 2009

An Introduction to Pseudospectra and their Applications

Lecture 1

The program for the first day is as follows:

Introduction. Presentations of participants. Formalities regarding the course.
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.
Coffee break.
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.
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.


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:

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Updated 09/09/2009, 14:55