# Mitja Nedić: An integral representation for Herglotz-Nevanlinna functions in several variables and its consequences

Source: Complex analysis seminar

Title: An integral representation for Herglotz-Nevanlinna functions in several variables and its consequences.

Abstract: Herglotz-Nevanlinna functions are holomorphic functions defined in the poly-upper half-plane having non-negative imaginary part. When considering the case of one complex variable, this is an old topic that has first been considered by Herglotz, Nevanlinna, Pick and others around 100 years ago. Partial results for the several variable case have been known since the 1970s, but no complete characterization of this class of functions has been given before now. In this talk, we will first present a complete characterization of the class of Herglotz-Nevanlinna functions in several variables via an integral representation involving a real constant, a liner part, a given integral kernel and a positive Borel measure. Afterwards, consequences of this integral representations will be investigated, focusing mainly on the class of boundary measures of Herglotz-Nevanlinna functions.

Seminar bo v predavalnici 3.06 na Jadranski 21. Vljudno vabljeni!

Vodji seminarja

Josip Globevnik in Franc Forstnerič