Higher-order interlacing for matrix-valued meromorphic Herglotz functions
Complex Variables
2022-05-02 v3
Abstract
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 property. As an application we deduce a matrix version of the classical Hermite-Biehler Theorem for entire functions.
Cite
@article{arxiv.2108.10746,
title = {Higher-order interlacing for matrix-valued meromorphic Herglotz functions},
author = {Jakob Reiffenstein},
journal= {arXiv preprint arXiv:2108.10746},
year = {2022}
}
Comments
17 pages, 0 figures