Hilbert space methods
Vorlesung im Sommersemester 2008 an der TU Chemnitz (in englischer Sprache)Coordinates:
Mi 2., N 002
Hilbert spaces are an important mathematical tool, both in theory and applications. They are the simplest examples of infinite dimensional spaces and provide the foundation of quantum physics. Both structure and applications of Hilbert spaces will be presented in this course.
Content:1. Inner product spaces
2. Orthogonality and orthogonal projections
3. Orthonormal systems
4. Linear operators
5. Linear functionals and the Riesz representation theorem
6. Adjoints, unitaries and spectra
7. The spectra of bounded and selfadjoint operators
8. The spectral theorem, I: continuous functional calculus
9. Interlude: The Riesz-Markov Theorem
10. The spectral theorem, II: Multiplication operator form
11. The polar decomposition
12. Compact operators
Wer noch Fragen hat findet die Antwort ... hier References:
M. Reed and B. Simon: Methods of Modern Mathematical Physics I
J. Weidmann Lineare Operatoren in Hilberträumen I: Grundlagen