Spectral Theory
Lecture in the winter term 2009/2010 at the University of Technology Chemnitz
Coordinates:
Lecture Tue 17:15-18:45 2/B202
Exercise:
Carsten Schubert
.
Exercise sheets here
Content:
1. Foundations
1.1 Hilbert spaces
1.2 Operators
1.3 Measures (on locally compact spaces)
1.4 Spectrum and resolvent
1.5 Banach algebras
2. The spectral theorem
2.1 The (continuous) functional calculus and spectral measures
2.2 The spectral theorem - multiplication operators.
2.3 Projection valued measures and resolutions of the identity
2.4 Spectral types
3. The spectral theorem for unbounded operators
3.1 Selfadjoint and normal operators
3.2 Integration with respect to a spectral resolution
3.3 Herglotz' theorem and the spectral theorem
References:
P. Halmos: What does the spectral theorem say. here
Pedersen, Gert K.: Analysis now. Graduate Texts in Mathematics, 118. Springer-Verlag, New York, 1989.
Reed, Michael; Simon, Barry: Methods of modern mathematical physics. I. Functional analysis. Second edition. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980.
Weidmann, Joachim: Lineare Operatoren in Hilberträumen. Teil 1. (German) [Linear operators in Hilbert spaces. Part 1] Grundlagen. [Foundations] Mathematische Leitfäden. [Mathematical Textbooks] B. G. Teubner, Stuttgart, 2000.
