Higher-order interlacing for matrix-valued meromorphic Herglotz functions
Jakob Reiffenstein
TL;DR
This paper introduces a higher-order interlacing property to characterize matrix-valued Herglotz-Nevanlinna functions and extends classical theorems to matrix settings, enhancing understanding of their pole-zero structure.
Contribution
It provides a novel higher-order interlacing characterization for matrix-valued Herglotz-Nevanlinna functions and generalizes the Hermite-Biehler Theorem to matrices.
Findings
Characterization of matrix-valued Herglotz-Nevanlinna functions via higher-order interlacing
Derivation of a matrix version of the Hermite-Biehler Theorem
Extension of growth and pole-zero interlacing properties to matrix functions
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.