由振荡序列生成的带状矩阵的谱与精细谱
Spectrum and Fine Spectrum of Band Matrices Generated by Oscillatory Sequences
AI总结：
本文研究由振荡序列生成的新型带状矩阵，用紧扰动技术分析其在ℓₚ（1<p<∞）空间的谱，得到多种谱细分结果及本质谱上无点谱的充分条件。
摘要：
本文研究了一类新的带状矩阵，其每个非零带的元素构成具有两个极限点的序列。采用紧扰动技术研究该矩阵在ℓₚ（1<p<∞）序列空间上的谱，得到了精细谱、离散谱、本质谱等多种谱细分结果。此外，还讨论了本质谱上不存在点谱的若干充分条件。
英文摘要：
In this paper, a new class of band matrices is considered where the entries of each non-zero band form a sequence with two limit points. The compact perturbation technique is used to study the spectrum over the $\ell_{p}, (1<p<\infty)$ sequence space. Several spectral subdivisions such as fine spectrum, discrete spectrum, essential spectrum, etc. are obtained. In addition, a few sufficient conditions on the absence of point spectrum over the essential spectrum are also discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
