Mitja Nedic: Representing measures of Herglotz-Nevanlinna functions

Abstract:
A Herglotz-Nevanlinna function is a holomorphic function on the poly-upper half-plane having non-negative imaginary part. Every such function can be uniquely represented via a real number, a vector of non-negative numbers and a positive Borel measure. It is this measure, appropriately called the representing measure, that contains the most information about the function it represents.

In this talk, we investigate the properties of the class of representing measures of Herglotz-Nevanlinna functions. In particular, we shall investigate how the mass of certain subsets of n-dimensional Euclidean space is reflected in the function represented by the measure.

This talk is based on joint work with Annemarie Luger. The speaker is supported by the SSF grant AM13-0011.