Abstract
We consider unbounded, selfadjoint Jacobi matrices with weights λ n = n α(1+Δ n ), LimΔ n =0 and α \(\alpha \in (\frac{1} {2},1)\). The asymptotics for generalized eigenvectors of fixed energy is obtained. This allows to carry out, by using so called grouping in block method, analysis of absolutely continuous spectra of our class of operators. The main role play here algebraic properties of Pauli matrices arising in natural way in the analysis of corresponding transfer matrices. It happenes that the commutation relations between Pauli matrices lead to the appearance of Cesaro-like averages in our study.
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Janas, J., Naboko, S. (2000). Asymptotics of Generalized Eigenvectors for Unbounded Jacobi Matrices with Power-like Weights, Pauli Matrices Commutation Relations and Cesaro Averaging. In: Adamyan, V.M., et al. Differential Operators and Related Topics. Operator Theory: Advances and Applications, vol 117. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8403-7_14
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DOI: https://doi.org/10.1007/978-3-0348-8403-7_14
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