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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 2017)

Lecturer: Prof. Dr. Tobias Lamm
Classes: Lecture (0163700), Problem class (0163710)
Weekly hours: 4+2


There will be no Exercise class on 27.07.2017.

Schedule
Lecture: Monday 9:45-11:15 SR 2.66 Begin: 24.4.2017, End: 26.7.2017
Wednesday 9:45-11:15 SR 2.66
Problem class: Thursday 14:00-15:30 SR 2.67
Lecturers
Lecturer, Problem classes Prof. Dr. Tobias Lamm
Office hours:
Room 2.040 Kollegiengebäude Mathematik (20.30)
Email: tobias.lamm@kit.edu
Problem classes M. Sc. Michael Ullmann
Office hours: Whenever you want
Room 2.033/ 2.034 Kollegiengebäude Mathematik (20.30)
Email: michael.ullmann@kit.edu

In this lecture we extend the spectral theory for compact operators, which we derived in the Functional Analysis course, to unbounded operators on Hilbert spaces. Then we apply these results in order to study Schrödinger operators and the eigenvalues of the Laplace operator in bounded domains.

The lecture relies heavily on the Functional Analysis course taught in the winter term.

Exercise Sheets
Sometimes there will be an exercise sheet, but perhaps not every week, which you can find here on the webpage.
You can hand in your solution of every exercise and I (Michael) will correct it.
Please deliver your solution in the box on the ground floor of the math building or in the problem class.
In the problem class we will discuss the solutions and do some additional stuff.
1. Exercise Sheet Solutions to 1. Exercise Sheet
2. Exercise Sheet Solutions to 2. Exercise Sheet
3. Exercise Sheet
4. Exercise Sheet Some remarks to the Exercise Class for Exercise Sheet 4


Examination

There will be oral exams on three days in october (11.10., 12.10. and 13.10.).
From tuesday onwards you will find a list in the office of Kaori Nagato-Plum, please choose there your favourite date and slot.
But don't forget to register online for the exam.
If there are any problems, please come to Michael Ullmann or write an E-Mail.

References

  • E.B. Davies: Spectral theory and differential operators
  • B. Helffer: Spectral theory and its applications
  • M. Reed, B. Simon: Methods of modern mathematical physics
  • G. Teschl: Mathematical methods in quantum mechanics. With applications to Schrödinger operators.