Abstract
We show a method of repairing some gaps in proofs of the absolute continuity of the spectrum of Jacobi operators. Such gaps have been found in several recent papers, dealing mainly with the so-called critical case (i.e., Jordan box case). We solve the problem by proving that the subordinate solution does not exist for many cases with two linearly independent generalised eigenvectors possessing “similar” asymptotic behaviour.
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The author would like to thank Professor Przemysław Wojtaszczyk for fruitful discussion and comments concerning the special kinds of convergence considered here. This paper is partially supported by grant N N201 605640 of Polish Ministry of Science and Higher Education.
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Moszyński, M. Non-Existence of Subordinate Solutions for Jacobi Operators in Some Critical Cases. Integr. Equ. Oper. Theory 75, 363–392 (2013). https://doi.org/10.1007/s00020-012-2018-0
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DOI: https://doi.org/10.1007/s00020-012-2018-0