On point spectrum of Jacobi matrices generated by iterations of quadratic polynomials

Fuente: arXiv
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Main Authors: Eichinger, Benjamin, Lukić, Milivoje, Yuditskii, Peter
Format: Preprint
Published: 2024
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_version_ 1866916890698317824
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
id 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