Mitja Nedic: A survey on the interplay between Passive systems and Herglotz-Nevanlinna functions

Tid: On 2018-02-14 kl 11.00 - 12.00

Föreläsare: Mitja Nedic (SU)

Plats: Room 306, building 6 kräftriket, Department of Mathematics, Stockholm University

Many processes in nature can be modelled as a systems, i.e. a correspondence between a driving variable and a responding variable. Special types of these systems, called passive systems, are interesting because they are, in turn, modelled by operators on the space of distributions. This purely mathematical description of passive systems connects further to complex analysis via the Fourier or Laplace transforms, allowing us to analyse passive systems via holomorphic function theory.

In this survey talk, we present an overview of the mathematical modelling of passive systems and summarize the transition from the operator, modelling the system, to the corresponding Herglotz-Nevanlinna function, that is, a holomorphic function mapping the upper half-plane to the closed upper half-plane. We then review the properties of Herglotz-Nevanlinna functions that are commonly used to get information about the underlying passive system. Finally, we present some open questions in this area.