Work

A Weyl Matrix Perspective on Unbounded Non-Self-Adjoint Jacobi Matrices

Year: 2025

Type: article

Abstract: | together with a phase function was described by Pushnitski-Štampach in the bounded case. We present another perspective on this correspondence, based on Weyl functions instead of moments, which simplifies some proofs and generalizes the correspondence to the unbounded case. In particular, we find a bijection between proper Jacobi matrices with positive off-diagonal elements, and a class of spectral data. We prove that this mapping is continuous in a suitable sense. To prove injectivity of the map, we prove a local Borg-Marchenko theorem for unbounded non-self-adjoint Jacobi matrices in this class that may be of independent interest.

Source: Complex Analysis and Operator Theory

DOI: 10.1007/s11785-025-01804-5

Authors: Benjamin Eichinger, Milivoje Lukić, Giorgio Young

Institutions: Lancaster University, Rice University, University of Michigan

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: National Science Foundation, Austrian Science Fund