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Green Matrix Estimates of Block Jacobi Matrices II: Bounded Gap in the Essential Spectrum
Integral Equations and Operator Theory ( IF 0.8 ) Pub Date : 2020-05-23 , DOI: 10.1007/s00020-020-02576-7
Jan Janas , Sergey Naboko , Luis O. Silva

This paper provides decay bounds for Green matrices and generalized eigenvectors of block Jacobi operators when the real part of the spectral parameter lies in a bounded gap of the operator’s essential spectrum. The case of the spectral parameter being an eigenvalue is also considered. It is also shown that if the matrix entries commute, then the estimates can be refined. Finally, various examples of block Jacobi operators are given to illustrate the results.

中文翻译:

块 Jacobi 矩阵 II 的绿色矩阵估计:基本谱中的有界间隙

当谱参数的实部位于算子基本谱的有界间隙时,本文提供了格林矩阵的衰减界限和块雅可比算子的广义特征向量。还考虑了频谱参数是特征值的情况。还表明,如果矩阵条目交换,则可以改进估计。最后,给出了块 Jacobi 算子的各种例子来说明结果。
更新日期:2020-05-23
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