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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.11628 |
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| _version_ | 1866909581366525952 |
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| author | Levi, Netanel Malinovitch, Tal |
| author_facet | Levi, Netanel Malinovitch, Tal |
| contents | We study the spectral multiplicity of Jacobi operators on star-like graphs with $m$ branches. Recently, it was established that the multiplicity of the singular continuous spectrum is at most $m$. Building on these developments and using tools from the theory of generalized eigenfunction expansions, we improve this bound by showing that the singular continuous spectrum has multiplicity at most $m-1$. We also show that this bound is sharp, namely, we construct operators with purely singular continuous spectrum of multiplicity $m-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral Multiplicity Bounds for Jacobi Operators on Star-Like Graphs Levi, Netanel Malinovitch, Tal Spectral Theory 47B36 We study the spectral multiplicity of Jacobi operators on star-like graphs with $m$ branches. Recently, it was established that the multiplicity of the singular continuous spectrum is at most $m$. Building on these developments and using tools from the theory of generalized eigenfunction expansions, we improve this bound by showing that the singular continuous spectrum has multiplicity at most $m-1$. We also show that this bound is sharp, namely, we construct operators with purely singular continuous spectrum of multiplicity $m-1$. |
| title | Spectral Multiplicity Bounds for Jacobi Operators on Star-Like Graphs |
| topic | Spectral Theory 47B36 |
| url | https://arxiv.org/abs/2504.11628 |