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

2024/05/29 by Eichinger, Benjamin, Lukić, Milivoje, Yuditskii, Peter · 1 citation
#37C30 #37F15 (Secondary) #47B36 (Primary) 42C05 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2405.19470

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 z²-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.

Cited by

• Greenś Mapping and Julia Sets

Related

• Limit periodic Jacobi matrices with a singular continuous spectrum and the renormalization of periodic matrices
• Limit periodic Jacobi matrices with a prescribed p-adic hull and a singularly continuous spectrum
• Thin Spectra and Singular Continuous Spectral Measures for Limit-Periodic Jacobi Matrices
• Spectral and resonance problem for perturbations of periodic Jacobi operators
• If they are limit periodic?