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m-Functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices

Gesztesy, Fritz and Simon, Barry (1997) m-Functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices. Journal d'Analyse Mathématique, 73 (1). pp. 267-297. ISSN 0021-7670. https://resolver.caltech.edu/CaltechAUTHORS:20180110-165033558

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Abstract

We study inverse spectral analysis for finite and semi-infinite Jacobi matrices H. Our results include a new proof of the central result of the inverse theory (that the spectral measure determines H). We prove an extension of the theorem of Hochstadt (who proved the result in case n = N) that n eigenvalues of an N × N Jacobi matrix H can replace the first n matrix elements in determining H uniquely. We completely solve the inverse problem for (δ_n , (H-z)^(-1) δ_n ) in the case N < ∞.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/BF02788147DOIArticle
https://link.springer.com/article/10.1007/BF02788147PublisherArticle
http://rdcu.be/EsAKPublisherFree ReadCube access
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© Hebrew University of Jerusalem 1997. This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-9623121 and DMS-9401491.
Funders:
Funding AgencyGrant Number
NSFDMS-9623121
NSFDMS-9401491
Issue or Number:1
Record Number:CaltechAUTHORS:20180110-165033558
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180110-165033558
Official Citation:Gesztesy, F. & Simon, B. J. Anal. Math. (1997) 73: 267. https://doi.org/10.1007/BF02788147
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84241
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:11 Jan 2018 18:11
Last Modified:03 Oct 2019 19:16

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