Mitja Nedic: Symmetries of Herglotz-Nevanlinna functions in several variables

Abstract:
Herglotz-Nevanlinna functions are holomorphic functions on the poly-upper half-plane having non-negative imaginary part. For functions of one variable, a classic integral representation formula extends these functions to the lower half-plane. In addition, this extension possesses an interesting symmetry property.

In this talk, we investigate how the integral representation formula for Herglotz-Nevanlinna functions of several variables can be used to extend
these functions to the set of all complex vectors without any real entries. Furthermore, symmetry properties of this extended function are presented, as well as a result on the variable dependence of the extended function.

This talk is based on joint work with Annemarie Luger.