Complex Powers of Closed Operators

Dear Participants,

we close the investigation of well-posedness of evolution equations and turn our attention to more technical matters. As you may already know, our goal will be to be able to investigate the convergence behaviour of various discretisation procedures. To this end, some rather technical topics have to be covered. The first of these preparatory lectures deals with fractional powers, and can be downloaded by clicking on the PDF link below.

The idea is to construct spaces which are invariant under the semigroup and can be used to give estimates. If you are not familiar with the functional analytic ideas presented in this lecture, do not be afraid: the most important message is to know that we can define fractional powers and that they behave in a way as we expect.

We kindly ask the team of Tehran to present the official solutions for this week.

Best wishes and good reading,
your virtual lecturers

Alexander
András
Bálint
Petra

ISEM15_Lecture7.pdf

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

Discussion of Lecture 7.

Solutions and discussion of the exercises.