On point spectrum of Jacobi matrices generated by iterations of quadratic polynomials
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916890698317824 |
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| author | Eichinger, Benjamin Lukić, Milivoje Yuditskii, Peter |
| author_facet | Eichinger, Benjamin Lukić, Milivoje Yuditskii, Peter |
| contents | In general, point spectrum of an almost periodic Jacobi matrix can depend on the element of the hull. In this paper, we study the hull of the limit-periodic Jacobi matrix corresponding to the equilibrium measure of the Julia set of the polynomial $z^2-λ$ with large enough $λ$; this is the leading model in inverse spectral theory of ergodic operators with zero measure spectrum. We prove that every element of the hull has empty point spectrum. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_19470 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On point spectrum of Jacobi matrices generated by iterations of quadratic polynomials Eichinger, Benjamin Lukić, Milivoje Yuditskii, Peter Spectral Theory 47B36 (Primary) 42C05, 37C30, 37F15 (Secondary) In general, point spectrum of an almost periodic Jacobi matrix can depend on the element of the hull. In this paper, we study the hull of the limit-periodic Jacobi matrix corresponding to the equilibrium measure of the Julia set of the polynomial $z^2-λ$ with large enough $λ$; this is the leading model in inverse spectral theory of ergodic operators with zero measure spectrum. We prove that every element of the hull has empty point spectrum. |
| title | On point spectrum of Jacobi matrices generated by iterations of quadratic polynomials |
| topic | Spectral Theory 47B36 (Primary) 42C05, 37C30, 37F15 (Secondary) |
| url | https://arxiv.org/abs/2405.19470 |