# Christian Emmel: Pseudo-Nevanlinna functions

**Time: **
Fri 2021-10-22 13.15 - 14.15

**Location: **
Kräftriket 5, Room 32

**Lecturer: **
Christian Emmel (Stockholms Universitet)

**Abstract**

We will review classical results on ordinary Nevanlinna functions, in particular on their realization as operator resolvents. Based on that, Pseudo-Nevanlinna functions and their Indices are defined. In order to find resolvent type realizations in this generalized case, we must relax the definition of an inner product, which leads to the notion of Pontryagin and Krein spaces. These are introduced, and their main differences are illustrated. Finally, we come back to resolvent type realizations on these spaces.