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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.12685 |
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| _version_ | 1866917698352447488 |
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| author | Levi, Netanel |
| author_facet | Levi, Netanel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12685 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eigenfunction Expansion and the Decomposition of Jacobi Operators on $\mathbb{Z}$ Levi, Netanel Spectral Theory 47B36 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. |
| title | Eigenfunction Expansion and the Decomposition of Jacobi Operators on $\mathbb{Z}$ |
| topic | Spectral Theory 47B36 |
| url | https://arxiv.org/abs/2406.12685 |