Spectral Analysis of Selfadjoint Jacobi Matrices with Periodically Modulated Entries
Spectral Analysis of Selfadjoint Jacobi Matrices with Periodically Modulated Entries
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具有周期调制项的自伴雅可比矩阵的谱分析
DOI：
10.1006/jfan.2001.3866
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发表时间：
2002
影响因子：
1.7
通讯作者：
S. Naboko
中科院分区：
文献类型：
--
作者：
J. Janas;S. Naboko
本文研究了一类具有调制元的自伴无界Jacobi矩阵J的谱分析。条目具有平滑序列的形式，其增加到无穷大乘以适当的周期序列。对于这类谱，给出了谱的纯绝对连续性或离散性的判据，以及J的广义特征向量的渐近性。给出了一些说明谱结构稳定区的例子。
This paper deals with the spectral analysis of a class of selfadjoint unbounded Jacobi matrices J with modulated entries. The entries have the form of smooth sequences that increase to infinity multiplied by proper periodic sequences. For this class criteria for pure absolute continuity of the spectrum or its discreteness, and the asymptotics of generalized eigenvectors of J, are given. Some examples illustrating the stability zones of spectral structure are presented.