Green matrix estimates of block Jacobi matrices. II: Bounded gap in the essential spectrum. (English) Zbl 1442.15014
Summary: 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.
For Part I see [the authors, ibid. 90, No. 4, Paper No. 49, 24 p. (2018; Zbl 1442.15013)].
For Part I see [the authors, ibid. 90, No. 4, Paper No. 49, 24 p. (2018; Zbl 1442.15013)].
MSC:
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 39A22 | Growth, boundedness, comparison of solutions to difference equations |
| 47B36 | Jacobi (tridiagonal) operators (matrices) and generalizations |
| 33E30 | Other functions coming from differential, difference and integral equations |
Citations:
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