Rota universality of shifts on trees

We consider shift operators on infinite directed trees. We prove that under very mild assumptions on the structure of the tree, the resulting operator is universal (in the sense of Rota). We show connections between the spectrum of the operator and the frequency of branching in the tree.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.40089
Primary Topic
Holomorphic and Operator Theory
Type
preprint
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preprint

Rota universality of shifts on trees

Jeremiah Buckley, Daniel Seco
arXiv (Cornell University)
Holomorphic and Operator Theory
preprint

Rota universality of shifts on trees

Jeremiah Buckley, Daniel Seco
preprint en

Abstract

We consider shift operators on infinite directed trees. We prove that under very mild assumptions on the structure of the tree, the resulting operator is universal (in the sense of Rota). We show connections between the spectrum of the operator and the frequency of branching in the tree.

arXiv (Cornell University)
Holomorphic and Operator Theory
DOIOpen Access PDFOpenAlex
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Rota universality of shifts on trees — Jeremiah Buckley, Daniel Seco · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS