A characterization of Herglotz-Nevanlinna functions in two variables via integral representations (Q1692359)

Herglotz-Nevanlinna functions are functions that are analytic in the upper half-plane having non-negative real part. Let \(\mathbb{C}^{+2}=\{(z_1,z_2)\in\mathbb{C}^2: \Im(z_1) >0, \,\Im(z_2) >0\}\). In the paper under review the authors define the Herglotz-Nevanlinna function in two variables as a holomorphic function \(f:\mathbb{C}^{+2}\to\mathbb{C}\) with non-negative imaginary part. They derive an integral representation for these functions, thus giving a characterization of the class of Herglotz-Nevanlinna functions in two variables in terms of three real parameters, and in terms of a positive measure satisfying certain conditions.