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Functional Analysis and Its Applications

, Volume 41, Issue 2, pp 143–153 | Cite as

Meromorphic Jost functions and asymptotic expansions for Jacobi parameters

  • B. Simon
Article

Abstract

We show that the parameters a n , b n of a Jacobi matrix have a complete asymptotic expansion
$$a_n^2 - 1 = \sum\limits_{k = 1}^{K(R)} {p_k (n)\mu _k^{ - 2n} + O(R^{ - 2n} ),} b_n = \sum\limits_{k = 1}^{K(R)} {p_k (n)\mu _k^{ - 2n + 1} + O(R^{ - 2n} )} $$
, where 1 < |µj| < R for jK(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.

Key words

Jost function Jacobi matrix exponential decay 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • B. Simon
    • 1
  1. 1.California Institute of TechnologyPasadena

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