|Lecture:||Tuesday 9:45-11:15||1C-03||Begin: 16.4.2013|
|Problem class:||Wednesday 15:45-17:15||1C-03||Begin: 24.4.2013|
|Lecturer||Prof. Dr. Lutz Weis|
|Office hours: Friday, 11:45 to 13:15 and by appointment.|
|Room 2.042 Kollegiengebäude Mathematik (20.30)|
|Email: firstname.lastname@example.org||Problem classes||Dr. Markus Antoni|
|Office hours: by appointment|
|Room 2.044 Kollegiengebäude Mathematik (20.30)|
Spectral theory generalizes the theory of eigenvalues and normal forms of matrices to infinite dimensional operators on function spaces such as differential and integral operators. It provides an essential technique for many areas of applications such as partial differential 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
We assume a basic knowledge in functional analytic methods as provided by one of the courses
"Differentialgleichungen und Hilberträume" or "Funktionalanalysis".
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|
Additionally, you have to register for the exam via the QISPOS/Studierendenportal.
- 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