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 self-adjoint operators
  • Spectral theorem
  • Forms. Representation theorem.
  • Applications: self-adjoint differential operators and their spectral properties

Lecture
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.
  • Online-Kreuzerlsystem
  • Exercise sheets: Sheet 1, Sheet 2, Sheet 3, Sheet 4, Sheet 5, Sheet 6
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 self-adjoint 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, Springer-Verlag, New York-Berlin, 1980.

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, self-adjointness, Academic Press, New York, 1975