Cauchy Transforms of Colored Graphs in Two Variables
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908627329089536 |
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| author | Adlin, Lily Thai, Giovani Tiscareno, Samuel Tully-Doyle, Ryan |
| author_facet | Adlin, Lily Thai, Giovani Tiscareno, Samuel Tully-Doyle, Ryan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10695 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cauchy Transforms of Colored Graphs in Two Variables Adlin, Lily Thai, Giovani Tiscareno, Samuel Tully-Doyle, Ryan Complex Variables Functional Analysis 47A48, 05C50 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. |
| title | Cauchy Transforms of Colored Graphs in Two Variables |
| topic | Complex Variables Functional Analysis 47A48, 05C50 |
| url | https://arxiv.org/abs/2410.10695 |