Higher-order interlacing for matrix-valued meromorphic Herglotz functions
arXiv:2108.10746 · doi:10.1016/j.jmaa.2022.126260
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.
17 pages, 0 figures