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- W2896544588 abstract "The spectrum of three-diagonal self-adjoint p-periodic Jacobi matrix with positive off-diagonal elements an and real diagonal elements bn consists of p intervals separated by p−1 gaps γi, where some of the gaps can be degenerated. The following estimate is true ∑i=1p−1|γi|⩾max(max(4(a1...ap)1p,2maxan)−4minan,maxbn−minbn). We show that for any p∈N there are Jacobi matrices of minimal period p for which the spectral estimate is sharp. It is sharp for both: strongly and weakly oscillating (an), (bn). We call a periodic sequence (xn) weakly oscillating if maxxn≈minxn, and strongly oscillating if maxxn≫minxn. Moreover, the estimate improves some recently published spectral estimates." @default.
- W2896544588 created "2018-10-26" @default.
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- W2896544588 date "2019-06-01" @default.
- W2896544588 modified "2023-10-18" @default.
- W2896544588 title "A note on sharp spectral estimates for periodic Jacobi matrices" @default.
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- W2896544588 doi "https://doi.org/10.1016/j.jat.2019.03.003" @default.
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