Institut für Angewandte Mathematik

Lecture in Winter Term 2020/21 
Advanced Functional Analysis 
Content 
Lecture course covers various topic on unbounded operators and their spectral properties.
In particular, we will treat the following topics:
 Closed operators
 Spectrum, resolvent
 Symmetric and selfadjoint operators
 Spectral theorem
 Forms. Representation theorem.
 Applications: selfadjoint differential operators and their spectral properties

Lecture 
 Dr. Markus Holzmann
 The schedule for the lecture can be found in the TUGonline
 OnlineKreuzerlsystem for contact tracing lists for the lecture
 If the lecture can not be done in the seminar room at the University due to the Covid 19 situation, videos will be provided, where the content will be explained.
 Links to recordings of lectures: 12.10.2020, 9.11.2020, 10.11.2020, 16.11.2020, 23.11.2020, 24.11.2020, 30.11.2020, 7.12.2020, 14.12.2020, 11.1.2021, 18.1.2021, 19.1.2021, 25.1.2021
 End of Monday lectures:
 October 12: Chapter one of the lecture notes was finished
 October 19: Theorem 2.7  Definition 3.1 + remarks
 Notes for the next streamed lecture: January 25
 Notes of streamed lectures: November 9, November 10, November 16, November 23, November 24, November 30, December 7, December 14, January 11, January 18, January 19, January 25

Exercises 
 Dr. Markus Holzmann
 The schedule for the exercise classes can be found in the TUGonline
 Criteria for successful completion of the exercises:
 50% of the votes,
 two successful presentations at the blackboard of voted problems
 one half of the final mark is constituted by the votes and the other half by the presentations
 after two times voting for an exercise class students will get a grade
 If the exercise classes can not be done in the seminar room at the University due to the Covid 19 situation, the exercise class will be streamed via Webex.
 OnlineKreuzerlsystem
 Exercise sheets:
Sheet 1, Sheet 2, Sheet 3,
Sheet 4, Sheet 5, Sheet 6,
Sheet 7

Requirements 
Basic knowledges in functional analysis (Banach and Hilbert spaces,
linear bounded operators, weak and strong convergences etc.)

Literature 
Lecture notes:
Books:
 K.Schmüdgen, Unbounded selfadjoint operators on Hilbert space, Springer, Dordrecht, 2012.
 N.I.Akhiezer, I.M.Glazman, Theory of linear operators in Hilbert space, Dover Publications, Inc., New York, 1993.
 J.Weidmann, Linear operators in Hilbert spaces, SpringerVerlag, New YorkBerlin, 1980.
prüfungsaufs
Further reading:
 M.S.Birman, M.Z.Solomyak, Spectral theory of selfadjoint operators in Hilbert space, Reidel, Dordrecht, 1987
 T.Kato, Perturbation theory for linear operators, Springer, Berlin, 1995
 M.C.Reed, B.Simon, Methods of modern mathematical physics. I, second edition, Academic Press, New York, 1980; Methods of modern mathematical physics. II. Fourier analysis, selfadjointness, Academic Press, New York, 1975
