# Exercises

### From 15th ISeminar 2011/12 Operator Semigroups for Numerical Analysis

### **Exercises**

Dear Participants,

as announced, there is no lecture this week. Please use the time to review the material, next week we will continue with a long lecture again. We decided to pose some additional exercises to help you get accustomed with the material. You can access them by clicking on the PDF link below.

Many many thanks to all who contributed to the discussion on the homepage. Lot of mistakes got corrected and many aspects of the material got clarified. We will use this discussion to improve the manuscript. Thank you.

Finally, let us use this opportunity to speak of general references to operator semigroup theory. Our favorite is the introduction

- K. Engel, R. Nagel: A Short Course on Operator Semigroups Universitext. Springer-Verlag, New York, Berlin, Heidelberg, 2006.

We also make use of, among others, the following excellent texts:

- W. Arendt, C.J.K. Batty, M. Hieber, and F. Neubrander: Vector-valued Laplace transforms and Cauchy problems. Birkhäuser Verlag, Basel, 2001.
- J. A. Goldstein: Semigroups of Linear Operators and Applications. Oxford University Press, New York, 1985.
- A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, Berlin 1983.

We wish you all a good break.

Your virtual lecturers,

Alexander

András

Bálint

Petra

ISEM15_LectureC.pdf

Solutions and discussion of the **exercises**.

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