Lectures

Lectures will include the following topics:
  1. Introduction and basic techniques (perturbation results, numerical range etc. for unbounded linear operators)
  2. Unbounded block operator matrices (classification, criteria for closability/closedness, self-adjointness etc.)
  3. Block operator matrices associated with operators in Krein spaces and polynomial operator pencils
  4. Methods to investigate or enclose the spectrum (Schur complements, quadratic complements, quadratic numerical range)
  5. Advanced spectral properties (block diagonalization, solutions of Riccati equations, variational principles, Cauchy problems)
  6. Applications in mathematical physics (selected problems ranging from hydrodynamics to quantum mechanics).

Lecturers and Instructors

Heinz Langer

Prof. Dr. Heinz Langer (TU Vienna, Austria) is a leading expert in operator theory in spaces with an indefinite metric. He is the author of more than 200 scientific papers and the co-author of a well-known series of papers with the late M.G. Krein. He is a member of the editorial board of numerous mathematical journals and Corresponding Member of the Austrian Academy of Sciences. In many major international conferences in operator theory Prof. Langer serves as an invited keynote speaker.


Christiane Tretter

Prof. Dr. Christiane Tretter (University of Bern, Switzerland) is a leading expert in infinite dimensional block operator matrices. Last year she published the book Spectral Theory of Block Operator Matrices and Applications with Imperial College Press, London. Prof. Tretter has published more than 50 scientific papers and serves as the Editor-in-Chief of the international mathematical journal Integral Equations and Operator Theory (Birkhauser).


Matthias Langer

Dr. Matthias Langer is an experienced researcher in operator theory, in particular, in spctral theory for operator functions and block operator matrices. He is the coauthor of several papers together with Prof. H. Langer and Prof. C. Tretter. He is now Lecturer at the University of Strathclyde in Glasgow, United Kingdom.


Christian Wyss

Dr. Christian Wyss received his PhD in 2008 at the University of Bern. His research topics include Riccati equations, invariant subspaces and operators in spaces with an indefinite metric. At the moment he is holding a Post-Doc position at the University of Wuppertal.

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