Sommersemester 2020 Corona:

VL Funktionentheorie und Integraltransformationen

Die VL findet als Blockveranstaltung statt. Hoffentlich ist ab Juni 2020 Präsenzlehre möglich.

Wir fangen also erst sehr spät an, absolvieren aber dafür  7SWS die Woche.

Beginn: Donnerstag 4. Juni 2020.

Termine sind dann

Freitags 13:00- 17:15 (mit 2 Pausen)

Seminar Funktionalanalysis

Prof. Derkach and me offer for interested students a seminar in a selected topic in functional analysis.
Interested students select one of the following topics. If situation allows, we ask for a seminar talk as usual, otherwise for a summary in pdf, 10-20 pages. Please send me or Prof. Derkach an email if you are willing to join.

Main Topics:

Everitt, W. N. A note on the Dirichlet condition for second-order differential expressions. Canadian J. Math. 28 (1976), no. 2, 312–320.Evans, W. D.; Everitt, W. N. A return to the Hardy-Littlewood integral inequality. Proc. Roy. Soc. London Ser. A 380 (1982), no. 1779, 447–486.Evans, W. D.; Everitt, W. N. HELP inequalities for limit-circle and regular problems. Proc. Roy. Soc. London Ser. A 432 (1991), no. 1886, 367–390. 

2. Spectral Enclosures for a class of operator matrices. Related Papers:

J. Giribet, M. Langer, F. Peria, F. Philipp, C. Trunk, to appear in J. Funct. Anal.

Additional:
1. Spectral theorem for bounded and unbounded self-adjoint operators in Hilbert spaces (Kapitel VII.1 im Buch von Dirk Werner)
2. Bounded 2x2 operator matrices and their spectrum (C. Tretter, "Spectral Theory of Block Operator Matrices and Applications", Imperial College Press, 2008, Section 1.6 on Schur complements (but only Def. 1.6.1, Prop. 1.6.2, and Thm. 1.6.3), AND Section 1.13 Gershgorin's theorem for block operator matrices).
3. Spectrum and resolvent of unbounded 2x2 operator matrices(Tretter's book, Section 2.3).
4. The essential spectrum of unbounded 2x2 operator matrices(Tretter's book, Section 2.4).
5. The class of  Herglotz-Nevanlinna functions,  Kac subclasses and their integral representations. Related Papers:
I.~S. Kac and M.~G. Krein. R-functions -- analytic functions mapping the upper halfplane into itself. Amer. Math. Soc. Transl. Ser. 2, 103 (1974),  1--18.
N.~Aronszajn and W.~F. Donoghue. On the exponential representations of analytic functions in the upper half-plane with positive imaginary part. d'Analyse Math. 5:321--388, 1956.