A discrete Levinson theorem for systems with singular limit and estimates of generalized eigenvectors of some Jacobi operators

Moszyński M.

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A discrete Levinson theorem for systems with singular limit and estimates of generalized eigenvectors of some Jacobi operators

机译：具有奇异极限的系统的离散Levinson定理和某些Jacobi算子的广义特征向量的估计

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We prove a discrete Levinson type theorem on asymptotic properties of solutions of discrete d-dimensional systems with being bounded variation sequence and with the perturbation being 'appropriately small', for the case when has zero eigenvalue. We use this result to obtain estimates for some generalized eigenvectors of Jacobi operators. In particular we get estimates of the eigenvectors decay for Jacobi matrices with 'shaky weights'.

机译：我们证明了离散d维系统解的渐近性质的离散Levinson型定理，该问题具有有界变化序列，并且摄动为“适当小”（对于零特征值的情况）。我们使用这个结果来获得对Jacobi算子的一些广义特征向量的估计。特别是，我们获得了具有“抖动权重”的Jacobi矩阵的特征向量衰减的估计。

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来源
《Journal of difference equations and applications》 |2013年第8期|共17页
作者
Moszyński M.;
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原文格式 PDF
正文语种 eng
中图分类 51.63;
关键词
asymptotic behaviour of solutions; discrete and point spectrum; generalized eigenvectors; linear systems of difference equations; spectral analysis of Jacobi operators/matrices; the Levinson theorem;

机译：解的渐近行为;离散和点谱;广义特征向量;差分方程的线性系统;Jacobi算子/矩阵的谱分析;Levinson定理;

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A discrete Levinson theorem for systems with singular limit and estimates of generalized eigenvectors of some Jacobi operators

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