Abstract
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.
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Acknowledgements
The authors thank the anonymous reviewer for pertinent and useful comments and remarks which led to an improved version of the manuscript. S N was supported by Grant RFBR 19-01-00657 A (Sections 1–4) and Grant RScF 20-11-20032 (Sections 5–6). He expresses his gratitute to the Institut Mittag-Leffler, where part of this work has been done, for their kind hospitality and to the Knut and Alice Wallenberg Foundation for the support given. L O S has been supported by UNAM-DGAPA-PAPIIT IN110818 and SEP-CONACYT CB-2015 254062. Part of this work was carried out while L O S was on sabbatical leave at the University of Bath from UNAM with the support of PASPA-DGAPA-UNAM.
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Janas, J., Naboko, S. & Silva, L.O. Green Matrix Estimates of Block Jacobi Matrices II: Bounded Gap in the Essential Spectrum. Integr. Equ. Oper. Theory 92, 21 (2020). https://doi.org/10.1007/s00020-020-02576-7
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DOI: https://doi.org/10.1007/s00020-020-02576-7