Eigenfunction Expansion and the Decomposition of Jacobi Operators on $\mathbb{Z}$

Netanel Levi

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arXiv · 2406.12685

Eigenfunction Expansion and the Decomposition of Jacobi Operators on $\mathbb{Z}$

Netanel Levi

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Abstract

Let $J$ be a Jacobi operator on $\ell^2\left(\mathbb{Z}\right)$. We prove an eigenfunction expansion theorem for the singular part of $J$ using subordinate solutions to the eigenvalue equation. We exploit this theorem in order to show that $J$ can be decomposed as a direct integral of half-line operators.

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BibTeX RIS

Netanel Levi. 2024-06-18. Eigenfunction Expansion and the Decomposition of Jacobi Operators on $\mathbb{Z}$. https://arxiv.org/abs/2406.12685

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