TUHH / Institut für Mathematik / Mitarbeiter / Prof. Dr. Marko Lindner / Projekte Englische Flagge


Wave Scattering in Unbounded Domains: Operator Algebra and Limit Operator Techniques (2005-2007)

This project (led jointly with S. N. Chandler-Wilde) was supported by the EU with EUR 155k (Individual Marie-Curie Fellowship).

Spectra, Fredholm Properties and Stable Approximation of Infinite Matrices (2008-2011)

This project was supported by the EU with EUR 45k (Individual Marie-Curie Grant).

The aim of the project was twofold:

  1. Marie Curie Actions To extend the theoretical results on the Fredholm- and spectral theory as well as on the numerical analysis of the rather general class of operator equations studied in the previous project. After the explicit (and practically relevant) description of the essential spectrum, the focus is now on the whole spectrum as well as on pseudospectra for very general non-selfadjoint operators. On the numerical side, we want to better understand and appropriately modify (in the case of non-stability) the truncation methods studied before.
  2. Our motivation for this research and the focus of the second part of this project is the application of our theory to concrete problems in mathematical physics and population biology. Here we mention the acoustic scattering problems from the first project and concrete problems from quantum physics such as the Anderson model and its non-selfadjoint versions by Hatano & Nelson, the randomly hopping particle model by Feinberg & Zee, and the study of discrete Schrödinger operators with random, almost periodic or slowly oscillating potential.