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Workgroup Applied Analysis

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 2.029

Address
Englerstrasse 2
76131 Karlsruhe
Germany

Dr. Kaori Nagato-Plum
kaori.nagatou@kit.edu




Office hours:
Mon - Fri 10:00 -- 12:00

Tel.: +49 721 608 42056

Fax.: +49 721 608 46214

Spectral Theory (Summer Semester 2019)

Lecturer: PD 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 PD 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

Summary of the Lecture

The summary (version 24.07.19) will be constantly updated.


Exercise sheets

1st exercise Solutions
2nd exercise Solutions
3rd exercise Solutions
4th exercise Solutions
5th exercise Solutions
6th exercise Solutions
7th exercise Solutions
8th exercise Solutions
9th exercise Solutions
10th exercise Solutions
11th exercise Solutions
12th exercise

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.