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Journal d’Analyse Mathématique

, Volume 73, Issue 1, pp 267–297 | Cite as

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

  • Fritz Gesztesy
  • Barry Simon
Article

Abstract

We study inverse spectral analysis for finite and semi-infinite Jacobi matricesH. Our results include a new proof of the central result of the inverse theory (that the spectral measure determinesH). We prove an extension of the theorem of Hochstadt (who proved the result in casen = N) thatn eigenvalues of anN × N Jacobi matrixH can replace the firstn matrix elements in determiningH uniquely. We completely solve the inverse problem for (δ n , (H-z)-1 δ n ) in the caseN < ∞.

Keywords

Inverse Problem Jacobi Matrix Spectral Measure Trace Formula Jacobi Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University of Jerusalem 1997

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Division of Physics, Mathematics, and AstronomyCalifornia Institute of TechnologyPasadenaUSA

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