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ON THE EXISTENCE OF WKB-TYPE ASYMPTOTICS FOR THE GENERALIZED EIGENVECTORS OF DISCRETE STRING OPERATORS
Published online by Cambridge University Press: 02 February 2004
Abstract
Let $J$ be a Jacobi real symmetric matrix on $l_{2}$ with zero diagonal and non-diagonal entries of the form $\{1+p_{n}\}$. If $p_{n-1}\pm p_{n}=O(n^{-\alpha})$ with some $\alpha>2/3$, then the existence of bounded solutions of $Ju=\lambda u$ is proved for almost every $\lambda\in(-2,2)$ with the WKB-type asymptotic behavior.
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- © The London Mathematical Society 2004
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