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Published May 12, 2007 | public
Journal Article

Meromorphic Jost functions and asymptotic expansions for Jacobi parameters

Simon, B. ORCID icon

Abstract

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.

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.

Additional details

Created:
August 22, 2023
Modified:
October 26, 2023