Higher-order interlacing for matrix-valued meromorphic Herglotz functions

Scalar-valued meromorphic Herglotz-Nevanlinna functions are characterized by the interlacing property of their poles and zeros together with some growth properties. We give a characterization of matrix-valued Herglotz-Nevanlinna functions by means of a higher-order interlacing condition. As an application we deduce a matrix version of the classical Hermite-Biehler Theorem for entire functions. (C) 2022 The Author(s). Published by Elsevier Inc.

Automated summary

This article presents the characterization of Herglotz-Nevanlinna functions and the matrix version of the Hermite-Biehler Theorem. These results are of great significance in studying the properties of functions.