Teaching summer semester 2020
Lecture (4 SWS) "Functional analysis II - Spectral theory in Hilbert spaces"
Description:
In your linear algebra course you have learned that every hermitian matrix admits a basis of orthogonal
eigenvectors associated with real-valued eigenvalues. In our course we focus on generalizations in the
framework of self-adjoint operators on Hilbert spaces. Starting out with compact operators we'll work
towards our main goal, which is the spectral theorem for unbounded self-adjoint operators and some
impactful mathematical applications.
Target group:
Diploma and master students. Students enrolled in the master program ``Mathematical Physics'' may get
credit for the module 10-MAT-MPFOP2 if they successfully give a talk in a related seminar within the
master program. Students who would like to do that should contact me in advance.
Prerequisites:
pre-diploma in mathematics, basic measure theory, basic knowledge on functional analysis,
in particular on normed spaces, Hilbert spaces and bounded operators.
And most importantly of course, having fun learning new maths! ;)
Note: this course will be held in English.
Coordinates if/when classes resume:
Mon 13:15-14:45 and Tue 11:15-12:45 in SG 2-14.
Until we can meet again in person you will be provided with learning material that is designed
for self-study and will serve as a basis for your communication with your fellow participants
and with the instructor. Please reserve the above time slots for virtual interactions.
You are in? Great, just sign up for the moodle course! If you have any questions, send me an email.
Recommended literature:
Conway, John B.: A Course in Functional Analysis
Graduate Text in Mathematics, Springer New York.
Reed, Michael and Simon, Barry: Methods of Modern Mathematical Physics I: Functional Analysis.
Academic Press New York and London.
Reed, Michael and Simon, Barry: Methods of Modern Mathematical Physics II: Fourier analysis, self-adjointness.
Academic Press New York and London.
Reed, Michael and Simon, Barry: Methods of Modern Mathematical Physics IV: Analysis of operators.
Academic Press New York and London.
Pedersen, Gert K.: Analysis Now.
Springer New York.
Schmüdgen, Konrad: Spectral theory of Unbounded Self-adjoint operators of Hilbert space.
Graduate Text in Mathematics, Springer Heidelberg New York London.
Weidmann, Joachim: Lineare Operatoren in Hilberträumen I: Grundlagen. (for German speakers)
Teubner Stuttgart Leipzig Wiesbaden.
Werner, Dirk: Funktionalanalysis. (for German speakers)
Springer Spektrum Berlin.