We consider an infinite lower triangular matrix, which is a difference operator, with three bands formed by oscillatory sequences. We show that the matrix is a bounded linear operator over the space \(c_0\). We determine the spectrum and its subdivisions of the matrix over \(c_0\). Then, we generalize the matrix to a \((p+1)\)th band infinite lower triangular matrix. We give an estimation of the spectrum of this generalized matrix. Finally, we compare our results with other standard estimations.

中文翻译：

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由振荡序列形成的下三角无限矩阵的光谱

我们考虑一个无限的下三角矩阵，它是一个差分算子，具有由振荡序列形成的三个频带。我们证明矩阵是空间\(c_0\) 上的有界线性算子。我们确定\（c_0 \）上矩阵的频谱及其细分。然后，我们将矩阵推广到第\((p+1)\)个带无限下三角矩阵。我们给出了这个广义矩阵的频谱估计。最后，我们将我们的结果与其他标准估计进行比较。