An integral representation for Herglotz-Nevanlinna functions in several variables

Abstract

In this article, a characterization of the class of Herglotz-Nevanlinna functions in $n$ variables is given in terms of an integral representation. Furthermore, alternative conditions on the measure appearing in this representation are discussed in detail. Symmetry properties induced by the integral representation are also investigated.

26 pages

References in corpus (1)

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

Cited by in corpus (6)

• Geometric properties of measures related to holomorphic functions having positive imaginary or real part
• A subclass of boundary measures and the convex combination problem for Herglotz-Nevanlinna functions in several variables
• On the structure of Nevanlinna measures
• Characterizations of Herglotz-Nevanlinna functions using positive semi-definite functions and the Nevanlinna kernel in several variables
• Herglotz-Nevanlinna matrix functions and Hurwitz stability of matrix polynomials
• Characterizations of the Lebesgue measure and product measures related to holomorphic functions having non-negative imaginary or real part