Jost functions and Jost solutions for Jacobi matrices, III. Asymptotic series for decay and meromorphicity

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dc.creatorSimon, Barry
dc.date2005-03-18
dc.date.accessioned2026-07-07T05:18:08Z
dc.date.available2026-07-07T05:18:08Z
dc.descriptionWe show that the parameters $a_n, b_n$ of a Jacobi matrix have a complete asymptotic series $ a_n^2 -1 &= \sum_{k=1}^{K(R)} p_k(n) μ_k^{-2n} + O(R^{-2n}) b_n &= \sum_{k=1}^{K(R)} p_k(n) μ_k^{-2n+1} + O(R^{-2n}) $ where $1 < |μ_j| < R$ for $j\leq K(R)$ and all $R$ if and only if the Jost function, $u$, written in terms of $z$ (where $E=z+z^{-1}$) is an entire meromorphic function. We relate the poles of $u$ to the $μ_j$'s.
dc.identifierhttps://arxiv.org/abs/math/0503392
dc.identifierhttp://arxiv.org/abs/math/0503392
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74553
dc.subjectSpectral Theory
dc.subject47B36, 81U40, 47A40
dc.titleJost functions and Jost solutions for Jacobi matrices, III. Asymptotic series for decay and meromorphicity
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