TL;DR
This paper investigates Jacobi matrices on infinite trees, establishing bounds on defect indices, criteria for selfadjointness, and constructing polynomial analogs, while also exploring nonnegativity conditions.
Contribution
It introduces new criteria for essential selfadjointness of Jacobi matrices on trees and constructs polynomial analogs, extending classical orthogonal polynomial theory to this setting.
Findings
Defect indices are at most 1 for these matrices.
Criteria for essential selfadjointness are provided.
Conditions for nonnegativity are analyzed.
Abstract
We study Jacobi matrices on trees with one end at inifinity. We show that the defect indices cannot be greater than 1 and give criteria for essential selfadjointness. We construct certain polynomials associated with matrices, which mimic orthogonal polynomials in the classical case. Nonnegativity of Jacobi matrices is studied as well.
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