Work

Cauchy transforms of colored graphs in two variables

Year: 2025

Type: article

Abstract: By designating vertices with variables, a simple undirected graph can be augmented to have 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.

Source: Linear Algebra and its Applications

DOI: 10.1016/j.laa.2025.11.002

Authors: Lily Adlin, Giovani Thai, Samuel Tiscareno, Ryan Tully-Doyle

Institution: California Polytechnic State University

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,230

Funders: National Science Foundation, Directorate for Mathematical and Physical Sciences, College of Science and Mathematics, Cal Poly San Luis Obispo