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Workgroup Functional Analysis

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 2.041

Address
Karlsruher Institut für Technologie
Institut für Analysis
Englerstraße 2
76131 Karlsruhe


samira.junge@kit.edu, natascha.katz@kit.edu


Office hours:
9:00 - 11:00

Tel.: +49 721 608 43727

Fax.: +49 721 608 67650

Spectral Theory (Summer Semester 2013)

Lecturer: Prof. Dr. Lutz Weis, Dr. Markus Antoni
Classes: Lecture (0156400), Problem class (0156500)
Weekly hours: 4+2


Schedule
Lecture: Tuesday 9:45-11:15 1C-03 Begin: 16.4.2013
Friday 9:45-11:15 1C-03
Problem class: Wednesday 15:45-17:15 1C-03 Begin: 24.4.2013
Lecturers
Lecturer Prof. Dr. Lutz Weis
Office hours: Friday, 11:45 to 13:15 and by appointment.
Room 2.042 Kollegiengebäude Mathematik (20.30)
Email: lutz.weis@kit.edu
Problem classes Dr. Markus Antoni
Office hours: by appointment
Room 2.044 Kollegiengebäude Mathematik (20.30)
Email: markus.antoni@kit.edu

Spectral theory generalizes the theory of eigenvalues and normal forms of matrices to in finite dimensional operators on function spaces such as di fferential and integral operators. It provides an essential technique for many areas of applications such as partial diff erential equations, mathematical physics and numerical analysis.

We will cover

  • spectra and resolvents of linear (unbounded) operators,
  • the spectral theory of compact operators and the Fredholm alternative,
  • the functional calculus of self-adjoint operators,
  • the holomorphic functional calculus of sectorial operators,
  • the Cauchy problem for sectorial operators.

This lecture will prepare for further courses or seminars on deterministic and stochastic evolution
equations.


Prerequisites
We assume a basic knowledge in functional analytic methods as provided by one of the courses
"Di fferentialgleichungen und Hilberträume" or "Funktionalanalysis".


Exercise Sheets

Exercise Sheet 1 Exercise 2 b)
Exercise Sheet 2 Solutions 2
Exercise Sheet 3 Exercise 6 b)
Exercise Sheet 4 Exercise 11
Exercise Sheet 5 Exercise 13 b)
Exercise Sheet 6
Exercise Sheet 7 Exercise 20
Exercise Sheet 8 Exercise 23 b)
Exercise Sheet 9
Exercise Sheet 10
Exercise Sheet 11
Exercise Sheet 12 Exercise 35
Exercise Sheet 13 Exercises 37 and 40

Examination

The exam in Spectral Theory will be oral and can be either in English or in German. It will take place on the following dates:

Thursday, July 25, 2013
Friday, July 26, 2013
Wednesday, October 9, 2013
Thursday, October 10, 2013
Friday, October 11, 2013

Please contact either Mrs Fuchs or Mr Antoni to arrange an appointment on the above dates or if you have any comments or questions on the exam.

Additionally, you have to register for the exam via the QISPOS/Studierendenportal.


References

  • J.B. Conway: A Course in Functional Analysis, Springer
  • M. Reed, B. Simon: Methods of modern mathematical physics, volume 1: Functional analysis, Academic Press
  • D. Werner: Funktionalanalysis, Springer