Cauchy Transforms of Colored Graphs in Two Variables
Complex Variables
2025-11-05 v2 Functional Analysis
Abstract
By designating vertices with variables, a simple undirected graph can be augmented to have an associated representing rational function in two variables taking the complex bi-upper halfplane to itself. We give relations between representing functions of certain products of such graphs by way of Schur complements. We also study the connection between the structure of the graph and the regularity of the representing function at a boundary singularity.
Cite
@article{arxiv.2410.10695,
title = {Cauchy Transforms of Colored Graphs in Two Variables},
author = {Lily Adlin and Giovani Thai and Samuel Tiscareno and Ryan Tully-Doyle},
journal= {arXiv preprint arXiv:2410.10695},
year = {2025}
}