Annemarie Luger: On Quasi-Herglotz functions

Abstract

Herglotz–Nevanlinna functions, by definition functions that map the upper half-plane analytically into itself, are very well known and this set forms a cone.

The class of Quasi-Herglotz functions is then defined as the set of all linear combinations of Herglotz–Nevanlinna functions. Despite its simple definition this class exhibits interesting properties, which will be discussed.

This talk is based on joint work with Mitja Nedic.