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arXiv · 2405.19470

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

Benjamin Eichinger·Milivoje Lukić·Peter Yuditskii
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Abstract

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 $z^2-\lambda$ with large enough $\lambda$; 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.

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Benjamin Eichinger, Milivoje Lukić, Peter Yuditskii. 2024-05-29. On point spectrum of Jacobi matrices generated by iterations of quadratic polynomials. https://arxiv.org/abs/2405.19470

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