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Funktsional. Anal. i Prilozhen., 2007, Volume 41, Issue 2, Pages 78–92 (Mi faa2862)  

This article is cited in 3 scientific papers (total in 3 papers)

Meromorphic Jost Functions and Asymptotic Expansions for Jacobi Parameters

B. Simon

California Institute of Technology

Abstract: We show that the parameters $a_n$, $b_n$ of a Jacobi matrix have a complete asymptotic expansion
$$ a_n^2-1=\sum_{k=1}^{K(R)} p_k(n) \mu_k^{-2n}+ O(R^{-2n}),\qquad b_n=\sum_{k=1}^{K(R)} p_k(n)\mu_k^{-2n+1}+O(R^{-2n}), $$
where $1<|\mu_j|<R$ for $j\le K(R)$ 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 $\mu_j$'s.

Keywords: Jost function, Jacobi matrix, exponential decay

DOI: https://doi.org/10.4213/faa2862

Full text: PDF file (238 kB)
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English version:
Functional Analysis and Its Applications, 2007, 41:2, 143–153

Bibliographic databases:

UDC: 517.98
Received: 12.05.2006

Citation: B. Simon, “Meromorphic Jost Functions and Asymptotic Expansions for Jacobi Parameters”, Funktsional. Anal. i Prilozhen., 41:2 (2007), 78–92; Funct. Anal. Appl., 41:2 (2007), 143–153

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Killip R., “Spectral theory via sum rules”, Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday - ERGODIC SCHRODINGER OPERATORS, SINGULAR SPECTRUM, ORTHOGONAL POLYNOMIALS, AND INVERSE SPECTRAL THEORY, Proceedings of Symposia in Pure Mathematics, 76, no. 2, 2007, 907–930  crossref  mathscinet  zmath  adsnasa  isi
    2. Damanik D., Killip R., Simon B., “Perturbations of orthogonal polynomials with periodic recursion coefficients”, Ann. of Math. (2), 171:3 (2010), 1931–2010  crossref  mathscinet  zmath  isi  scopus
    3. Kozhan R., “Meromorphic Continuations of Finite Gap Herglotz Functions and Periodic Jacobi Matrices”, Commun. Math. Phys., 327:3 (2014), 921–950  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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