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Meromorphic Jost functions and asymptotic expansions for Jacobi parameters

Simon, B. (2007) Meromorphic Jost functions and asymptotic expansions for Jacobi parameters. Functional Analysis and its Applications, 41 (2). pp. 143-153. ISSN 0016-2663. doi:10.1007/s10688-007-0013-z.

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We show that the parameters ɑ_n, b_n of a Jacobi matrix have a complete asymptotic expansion ɑ^2_n − 1 = ∑_(k=1)^(K(R)) pk(n)μ^(−2n)_k + O(R^(−2n)),b_n = ∑_(k=1)^(K(R)) pk (n)μ^(−2n+1)_k + O(R^(−2n)), where 1 < |µ_j| < R for j ⩽ 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 µj’s.

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Simon, B.0000-0003-2561-8539
Additional Information:© by B. Simon, Original Russian Text Copyright. Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 41, No. 2, pp. 78–92, 2007. Received May 12, 2006. Supported in part by NSF grant DMS-0140592 and in part by grant No. 2002068 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.
Funding AgencyGrant Number
Binational Science Foundation (USA-Israel)2002068
Subject Keywords:Jost function; Jacobi matrix exponential decay
Issue or Number:2
Record Number:CaltechAUTHORS:20170809-102314012
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Official Citation:Simon, B. Funct Anal Its Appl (2007) 41: 143.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80011
Deposited By: Ruth Sustaita
Deposited On:09 Aug 2017 18:14
Last Modified:15 Nov 2021 17:52

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