Spectral Theory (Summer Semester 2019)
- Lecturer: apl. Prof. Dr. Peer Christian Kunstmann
- Classes: Lecture (0163700), Problem class (0163710)
- Weekly hours: 4+2
The topic of this course is the spectral theory of linear operators in Banach spaces. Spectral theory plays a role in the investigation of partial differential equations in various fields. Central topics are properties of the spectrum, the study of eigenvalues and eigenvectors, properties of the resolvent map, decompositions of the underlying space in invariant subspaces, and existence of functional calculi that allow, e.g., algebraic calculations with operators. We shall study in particular spectrum and resolvents of bounded and unbounded operators, the Fourier transform, Fredholm operators and perturbation theory, the spectral theorem for self-adjoint operators in Hilbert spaces, and applications to differential operators and boundary value problems.
Prerequisites: Functional Analysis, basics of Complex Analysis and Lebesgue integration
| Schedule | ||
|---|---|---|
| Lecture: | Tuesday 11:30-13:00 | SR 2.66 |
| Thursday 9:45-11:15 | SR 2.66 | |
| Problem class: | Monday 15:45-17:15 | SR -1.025 (UG) |
| Lecturers | ||
|---|---|---|
| Lecturer | apl. Prof. Dr. Peer Christian Kunstmann | |
| Office hours: Thursday, 13 - 14 Uhr | ||
| Room 2.027 Kollegiengebäude Mathematik (20.30) | ||
| Email: peer.kunstmann@kit.edu | Problem classes | Dr. Michal Jex |
| Office hours: | ||
| Room 2.030/2.031 Kollegiengebäude Mathematik (20.30) | ||
| Email: michal.jex@kit.edu | ||
Exercise sheets
References
J.B. Conway: A Course in Functional Analysis, Springer.
E.B. Davies: Spectral Theory and Differential Operators, Cambridge University Press.
N. Dunford, J.T. Schwartz: Linear Operators, Part I: General Theory, Wiley.
D.E. Edmunds, W.D. Evans: Spectral Theory and Differential Operators, Oxford University Press.
T. Kato: Perturbation Theory of Linear Operators, Springer.
S. Lang: Real and Functional Analysis, Springer.
R. Meise, D. Vogt: Introduction to Functional Analysis, Oxford, Clarendon Press.
W. Rudin: Functional Analysis, McGraw-Hill.
D. Werner: Funktionalanalysis, Springer.