Research

Prof. Dr. Carsten Trunk is interested in a special structure: While distances are usually positive, he is interested in what happens if you also allow negative distances. In this case, for example, two different points can have a distance of zero from each other. Surprisingly, such spaces appear in many problems, such as modern quantum mechanics or hydrodynamics. Besides his research in the field of applied functional analysis, Prof. Trunk has been giving lectures for engineers for many years.

AnLi Fotografie

Prof. Dr. Carsten Trunk

  • Spectral and perturbation theory of self-adjoint operators in creine spaces
  • Spectral theory of operator functions
  • Differential equations
  • Problems of mathematical system theory
  • Eigenvalue problems for differential operators whose coefficients depend on the eigenvalue parameter
  • Problems of the extension theory of symmetric differential operators
  • Matrices in degenerate inner product spaces
  • Applications to indefinite Sturm-Liouville operators

Prof. Volodymyr Derkach

  • Extension theory of symmetric operators in Hilbert spaces,
  • Operators in indefinite inner product spaces
  • Perturbation theory
  • Interpolation problems of Pick-Nevanlinna type

The main results

PD Dr. Henrik Winkler

  • Structured perturbations of pencils related to electrical circuit design
  • DAE's and structures of linear relations
  • Spectral theory of systems of canonical differential equations, indefinite vibrating strings, and Sturm-Liouville equations
  • reproducing kernel Hilbert and Pontryagin spaces
  • generalized Nevanlinna functions, asymptotic expansions

Philipp Schmitz, M. Sc.

  • Sturm–Liouville Operators
  • Spectral Theory
  • Operator Theory
  • Differential Equations
  • Indefinite Inner Product Spaces
  • Perturbation Theory

Our courses

...are aimed at students of mathematics as well as students of computer science, technical physics and engineering. We attach great importance to high-quality, internationally oriented teaching, including English-language courses and study programmes.