Arkiv för Matematik

Volume 55 (2017)

Number 1

A characterization of Herglotz–Nevanlinna functions in two variables via integral representations

Pages: 199 – 216

DOI: https://dx.doi.org/10.4310/ARKIV.2017.v55.n1.a10

Authors

Annemarie Luger (Department of Mathematics, Stockholm University, Stockholm, Sweden)

Mitja Nedic (Department of Mathematics, Stockholm University, Stockholm, Sweden)

Abstract

We derive an integral representation for Herglotz–Nevanlinna functions in two variables, which provides a complete characterization of this class in terms of a real number, two non-negative numbers and a positive measure satisfying certain conditions. Further properties of the class of representing measures are also discussed.

Keywords

integral representation, Herglotz-Nevanlinna function, several complex variables

2010 Mathematics Subject Classification

30J99, 32A10, 32A26, 32A30, 32A40, 32A70

Full Text (PDF format)

The authors are supported by the SSF applied mathematics grant nr. AM13-0011.

Received 20 May 2016

Received revised 23 March 2017

Accepted 9 April 2017

Published 26 September 2017